Papers

We study the stabilizability of a N -level quantum systems using an indirect control ar- chitecture mediated by a noisy ancilla. After outlining the general theoretical framework for arbitrary N , we focus on the two-level case (N = 2), for which we derive a complete set of necessary and sufficient conditions for asymptotic stability. Finally, we illustrate the analyti- cal results with a simple numerical example on a two-spin system, showing convergence to a Bell state for a set of random initial conditions.

We study decentralized online optimization of upper-linearizable payoffs over an action set under efficient separation access, with applications to online continuous diminishing-return (DR) submodular maximization. We propose Decentralized Barrier Follow-the-Regularized-Leader (Dec-BFTRL), and evaluate each agent's played action against the average of all local objectives. Each agent maps an internal iterate to a feasible action through an approximate gauge projection, communicates only a cumulative surrogate-gradient dual state, and invokes the local HybridNewton procedure to approximately minimize its post-communication BFTRL potential. For every agent, we achieve expected network-aggregate regret of $\widetilde O(\sqrt{T})$. Over $T$ rounds, each agent uses $T$ neighbor-mixing steps and $\widetilde O(T)$ separation-oracle calls. We give wrapper instantiations covering four up-concave or DR-submodular maximization problems.

This paper presents a novel model-free algorithm for the finite-population linear quadratic Gaussian (LQG) decentralized social control problem with multiplicative noise. The state and control weights in the cost functional are not limited to be positive semidefinite. For both finite-horizon and infinite-horizon cases, the goal is to obtain a social optimum by solving two algebraic Riccati equations (AREs), without requiring prior knowledge of the system matrices. Then, we complete the design of a model-free algorithm for solving the decentralized social control problem. Especially, in the infinite-horizon case, the algorithm's convergence is based on analyzing the spectral property of the Lyapunov-type operator. The differences of reinforcement learning (RL) solutions between the finite-horizon and infinite-horizon cases are compared. Finally, the effectiveness of the proposed algorithm is demonstrated by a numerical example.

Stochastic programming (SP) is a powerful framework for decision-making under uncertainty, but its practical adoption in industry is often hindered by the difficulty in understanding the causal relationships that drive optimal solutions. In the two-stage SP, strategic first-stage decisions are coupled with operational second-stage recourse decisions. When the number of scenarios under consideration is large, understanding the direct link between the uncertainty realization and optimal recourse strategy becomes computationally and cognitively demanding. Common approaches to improve interpretability include trained classification trees or scenario reduction, replacing the large scenario set with a representative subset. This is often achieved through post-hoc clustering (e.g., k-means) based on uncertainty realizations or optimal recourse decisions. While useful, these methods only provide a statistical approximation of the solution space and may fail to reveal the underlying structural properties of the recourse problem that drive optimal first-stage decisions. This work introduces a novel, deterministic approach to explainability using multiparametric programming (mp) within a Benders decomposition framework. We reformulate the recourse subproblem as a multiparametric linear program, generating an explicit map of Critical Regions (CRs), which are polyhedral partitions of the uncertainty space. This allows us to cluster scenarios analytically rather than statistically. We demonstrate this methodology on a supply chain planning under demand uncertainty. Our results show that 100 stochastic scenarios map to exactly six critical region clusters. This mapping allows us to explain optimal capacity planning decisions as a precise trade-off between specific operational modes, providing a fully transparent interpretation of the stochastic solution.

Electrochemical distributed energy resources (DERs), such as electrolyzers and battery energy storage systems, consume large amounts of electricity. Buying that power directly from wholesale markets can sharply reduce operating costs. Accessing these markets, however, requires a minimum bid size that individual small or medium-scale units struggle to meet. Grouping several units to bid as a single participant clears this barrier while letting each unit use its own low-cost renewable generation. The common remedy is to hire a third-party aggregator, but aggregators charge commissions and solve a centralized optimization that often favors certain units over others. A fairer alternative is peer-to-peer (P2P) participation, where units form a self-governing group and bid jointly with no central authority. Because each self-interested unit is unwilling to share private data, coordination is best posed as a game-theoretic distributed optimization problem. Existing P2P methods, however, address only single-round spot markets and ignore the two-stage structure of real wholesale markets, where participants commit a day ahead and continuously adjust in real time. We close this gap with a two-stage receding-horizon generalized Nash equilibrium (GNE) game. Each unit re-optimizes its strategy every five minutes over a rolling one-hour horizon, while the group satisfies both market stages collectively. Units exchange only publicly visible aggregate power, never private cost or production data. We apply the approach to a six-unit fleet on the PJM market. It delivers 37% higher profit, 29% lower electricity cost, and 92% less renewable curtailment than individual participation, with every unit better off.

This work study a differential game of pursuit-evasion involving countably many pursuers $p_{1},p_{2},\cdots,p_{m}$ and a single evader $e$ under point-wise (geometric) constraints in the sequence space $l_{2}.$ The pursuers evolve according to specified differential equations of $1^{st}$ order while the evader follows a $2^{nd}$ order differential equation. The game period is a fixed time interval of length $\theta$ unit of time. The minimum distance between evader and the pursuer at the terminal time denotes the game payoff. The pursuers aim is to minimize the payoff, whereas the evader seeks to maximize it. We obtain the solution of the game, including optimal strategies of the players construction, as well as game value estimation.

We examine pursuit and evasion problems in the space $ \mathbb{R}^{n} $ involving a lone pursuer and evader. Motion of each player is governed by a first-order linear differential equation. The players' control functions are subject to the Gronwall-type inequality. The game's duration is fixed and represented by a positive number $\vartheta $. When the state of a pursuer coincides with that of the evader, we then say the pursuit is completed. On the contrary, evasion is possible when throughout the game there is no agreement between the states of pursuer and evader. The result obtained related to the pursuit problem depends on the attainability domains of the two players. On the other hand, one sufficient condition is given for evasion to be possible.

This paper investigates a multi-agent pursuit problem in which a group of pursuers seeks to intercept one or more evaders within a fixed operational time horizon. The motion of both pursuers and evaders is described by first-order linear differential equations, and the control inputs available to the agents are subject to Gronwall-type constraints. Pursuit is considered successful when at least one pursuer reaches the position of each evader at a finite time within the prescribed duration. Within this framework, we construct permissible strategies for the pursuers and derive sufficient conditions under which interception is guaranteed despite the evaders' counteractions. To support the theoretical results, we present numerical examples that demonstrate the effectiveness of the proposed strategies and confirm the analytical conditions for successful pursuit.

This paper introduces and studies the Multi-Objective Enterprise Green Supply Chain Network Design problem (MOEDGSCND) an extension of the well known Multi-Objective Supply Chain Network Design (MO-SCND), in this case a three-objective combinatorial optimisation problem that simultaneously minimises total cost f1, carbon dioxide emissions f2, and customer dissatisfaction f3 over binary decisions on which distribution centres to open and how to assign customer zones to open facilities. The problem generalises capacitated facility location and is known to be NP-hard. Furthermore this paper lays out a formal specification of decision variables, objective functions, all constraints and then investigates and compares three solution approaches using a single numerical instance: (A) exact weighted-sum integer linear programming solved via PuLP, (B) three Fully Polynomial-Time Approximation Schemes (FPTAS) providing (.94 + $\epsilon$)-guarantee approximations for $\epsilon$ := 0.15, and (C) two baseline heuristics for comparison. On an eight-customer, five-candidate-DC instance the exact solver certifies the optimal Pareto front across eight weight combinations, and all three FPTAS variants achieve their approximation guarantees, finishing within milliseconds compared to centiseconds for the exact ILP using the PuLP solver on this scale.

Under individual smoothness, known algorithms for nonconvex finite-sum optimization use $O(n+\sqrt n\Delta L_{\max}/\varepsilon^2)$ incremental first-order oracle (IFO) calls, while existing lower bounds miss the factor $\sqrt n$ in the second term. We prove the matching lower bound $\Omega(n+\sqrt n\Delta L_{\max}/\varepsilon^2)$ for randomized IFO algorithms, allowing component indices and query points to depend on the complete preceding history. Thus PAGE and SPIDER are minimax optimal up to universal constants under individual and mean-squared smoothness. Under the global Polyak-Lojasiewicz (PL) condition, prior lower bounds did not capture the correct dependence on $n$ under individual smoothness, and the regime of small $\kappa$ remained open for randomized IFO algorithms. We prove an $\Omega(n+\kappa_{\max}\sqrt n\log(\Delta/\varepsilon))$ lower bound for $\kappa_{\max}\ge\sqrt n$, and an $\Omega(n+n\log(\Delta/\varepsilon)/(1+\log(\sqrt n/\kappa_{\max})))$ lower bound for $3\le\kappa_{\max}\le\sqrt n$. Restarted PAGE attains matching upper bounds under mean-squared smoothness in terms of $\kappa_{\rm ms}=L_{\rm ms}/\mu$. Our lower bounds use dense weak hiding. Each hidden direction is spread across all components, making individual queries weakly informative while preserving the direction in the average. A sufficiently large dimension makes premature activation of future stages unlikely within the query budget. Balancing the cost of revealing a stage against the number of stages permitted by individual smoothness yields the missing $\sqrt n$ factor.

Given a finite set $A$ of natural numbers whose greatest common divisor is one, the Frobenius number $g(A)$ is the largest integer that is not a non-negative integer combination of the numbers in $A$. In a 2016 preprint, Matsubara states that given $A$ and $k$, deciding if $g(A) \geq k$ is $\Sigma_2^P$-complete. A decade has passed since without peer-reviewed publication of this result. At the same time, the community has found it difficult to verify this result. In this note, we give a write-up of the completeness proof based on Matsubara (2016).

Enforcing stochastic state constraints over the full prediction horizon in Model Predictive Control (MPC) can be computationally demanding. Here we study stochastic MPC without terminal ingredients in which chance constraints are enforced only over a shorter constraint horizon. Using stochastic relaxed dynamic programming, we derive an explicit upper bound on the average expected closed-loop cost that depends on both prediction and constraint horizons. For linear quadratic problems with affine chance constraints and bounded uniform disturbances, we provide a deterministic reformulation via coordinate transformation and constraint tightening. Simulations illustrate the trade-off between computational effort and performance.

Singularity degree is an important measure of semidefinite programming (SDP) degeneracy, but it is generally unavailable a priori from the problem data. We augment the Shor relaxation of nonempty binary sets $\{x\in\{0,1\}^n:Ax=b\}$ with the first-level Reformulation-Linearization Technique (RLT) equations generated by the defining linear equalities. For the resulting equality-generated SDP-RLT relaxation, we determine the exact worst-case singularity degree. If $\operatorname{rank}(A)=m$ and $0<m<n$, then the associated relaxation has singularity degree at most $\min\{m,n-m\}$, and this rank-nullity bound is attained for every possible rank in this range. Consequently, the worst-case singularity degree over this class is $\lfloor n/2\rfloor$ for $n\geq 2$. This is strikingly smaller than the sharp general bound $n$ for feasible SDP systems with matrix variables of order $n+1$ (Sturm, 2000, Example 2). Thus, for individual relaxations, rank and nullity provide an a priori bound on the otherwise inaccessible singularity degree and on the Hölder exponent in error bounds estimating distance to feasibility from constraint residuals.

This paper studies the identification of linearly parameterized nonlinear (LPN) systems. Although LPN systems share the same linear parameterization structure as linear systems, they are more challenging to identify. In particular, previous work has shown, through a counterexample based on a piecewise-affine system, that non-active exploration is generally insufficient for LPN system identification. In this paper, we consider LPN systems with real-analytic feature functions. We show that non-active exploration is sufficient for the identification of this class of systems by establishing non-asymptotic convergence rates of least-squares estimation and set-membership estimation. In addition, we provide counterexamples to show that non-active exploration may not be sufficient for system identification for non-real-analytic systems, even if those systems are infinitely differentiable. We present numerical experiments to further support and validate our theoretical results.

We introduce new notions of controllability and observability for networked linear time-invariant (LTI) systems based on $\sigma$-semistability of quiver representations. Utilizing King's criterion for $\sigma$-semistability, we define a network generalization of the Kalman decomposition for networked LTI systems, which systematically decomposes the local and interconnection dynamics while respecting the underlying network structure. Furthermore, we present efficient algorithms for deciding the proposed controllability and observability of a given networked LTI system and for finding the Kalman-type decomposition. We also show efficient algorithms for deciding the $\sigma$-semistability of representations of acyclic quivers with self-loops if the weight $\sigma$ has the same sign for all vertices with self-loops. Such quiver representations and weights arise from networked LTI systems.

Uncertainty quantification from finite data is central to machine learning, optimization, and automation systems, where decisions must remain reliable under limited samples and test-time distribution shift. Conformal prediction (CP) and distributionally robust optimization (DRO) offer two complementary approaches: CP constructs data-dependent prediction sets with distribution-free finite-sample validity under exchangeability, while DRO optimizes worst-case performance over an ambiguity set around an empirical distribution. We develop a unified probabilistic perspective on CP and DRO by viewing both as ways to turn finite calibration data into a data-dependent quantile estimator that a test score falls below with high probability. From this perspective, CP and DRO correct the empirical quantile along two coordinates of the same family of estimators: CP inflates the quantile level, whereas DRO shifts the quantile value through an ambiguity radius. Both methods provide the same calibration-conditional guarantee for the true distribution, requiring the target coverage to hold with high probability over the calibration sample. Their constructions differ, however: CP uses a closed-form, distribution-free level correction, while DRO uses a value-space correction whose certified radius depends on properties of the unknown distribution and additionally guarantees coverage uniformly over the ambiguity set. This distinction emerges in the tails of the score distribution. Because CP relies on sparse upper-tail order statistics of the calibration samples, its level inflation barely moves the estimator when those samples are dense near the target quantile but overshoots when they are sparse, whereas a well-chosen DRO radius corrects in value space and may avoid this overshoot.

The paper introduces a successive backstepping observer design for strictly feedforward parabolic PDE-ODE systems, in which the coupling structure determines the order of error stabilization and the corresponding transformations. First, a transformation based on a virtual measurement stabilizes the ODE observer error subsystem, which is most distal from the measurement, while decoupling it from the PDE error state. Second, a Volterra integral transformation is employed to stabilize the PDE error subsystem and to map the overall error dynamics into a cascade of exponentially stable ODE and PDE subsystems. The design is shown to be dual to a recently proposed multi-step state feedback design for parabolic PDE-ODE systems in strict feedback form, thus explaining the structure of the presented observer design.

Advances in machine learning (ML) have created new opportunities to complement traditional operations research (OR) methods. In particular, transformer models can capture complex interactions in token sequences by mapping tokens into a high-dimensional embedding space and propagating contextual information via attention. This makes them a candidate to model non-permutation flow shop scheduling with secondary resources as a next-token prediction task, where tokens represent job-machine-secondary resource tuples. For training, mixed-integer linear programming (MILP)-generated schedules are tokenized and used as next-token prediction data. During inference, partial token sequences (prefixes) are randomly generated and completed by the trained transformer through constrained decoding. A computational study is conducted on a flow shop with 8 jobs, 4 machines, and 3 secondary resources, where jobs are selected from a fixed pool of 20 jobs that is sampled during training and provides the candidates during prefix completion. The transformer achieves better solution quality (smaller makespans) compared to a genetic algorithm (GA), the NEH heuristic, and random search. It is outperformed only by the MILP model and the iterated greedy (IG) heuristic. The study concludes that transformer models can, to some extent, learn patterns from MILP-optimized non-permutation flow shop schedules and that transformer-based scheduling represents an interesting direction for future research, particularly in settings with a fixed, recurring job set.

Safety-critical optimization applications, such as real-time power system operation, maintain feasibility at every intermediate step, not merely at convergence. Existing approaches either violate constraints mid-solve (interior-point methods) or enforce feasibility through per-instant quadratic programming subproblems with cubic computational cost and unbounded worst-case execution time. We propose a continuous-time optimization framework for smooth constrained nonlinear problems that preserves feasibility throughout the optimization process without requiring projection operators, quadratic programming subproblems, or other per-iteration optimization routines. The method is built around a reciprocal multiplier manifold, which establishes an explicit relationship between inequality constraints and their associated Lagrange multipliers. By designing a continuous multiplier update law, the manifold is shown to remain forward invariant, while the resulting dynamics are equivalent to continuous-time logarithmic barrier gradient descent. The proposed framework naturally extends to multiple inequality constraints, equality constraints, nonconvex feasible sets, and infeasible initial conditions. The method is further enhanced through an augmented Uzawa flow that eliminates oscillatory transients commonly observed in classical primal-dual saddle-point dynamics. The effectiveness of the proposed approach is applied to the AC Optimal Power Flow problem of IEEE 9-bus and IEEE 57-bus systems. Numerical results show convergence to solutions within 0.4% of the benchmark optimum while maintaining strict feasibility of all constraints. A computational complexity analysis shows that the proposed dynamics reduce the per-step computational cost from cubic to linear complexity. Finally, dynamic tracking studies under time-varying operating conditions demonstrate reliable feasibility preservation.

The main focuses of the article are limit theorems of Wasserstein projection in the convex order which are useful for inference tasks. The main results rely on the establishment of dual attainment, stability and several useful observations. The first is a clean criterion to invoke the Wasserstein projection dualities on the classical cost $c=h(x-y)$. A new strategy was introduced to establish the dual attainment. Backward and forward dual transport are proved to enjoy a conjugate relationship. Sufficient conditions are given that ensure uniqueness of the optimal dual potential. These ingredients laid the groundwork for the proof of optimal dual potential stability, thereby permitting us to prove the central limit theorems under mild moment assumptions. Additional discussions show that the moment assumptions are sharp. These results also answered several open questions raised by Professor Benjamin Jourdain.

A company with a fixed artificial intelligence (AI) budget must decide which large language model (LLM) handles each recurring workload. What it lacks is the quality table, how well each model performs on each workload. Given that table, the decision is a multiple-choice knapsack problem and is routine to solve, so estimating it is the difficulty, and that estimation fails in two ways. Models are rarely compared on the same work, and the recorded score is usually a proxy rather than the outcome the company values. Causal and off-policy methods repair the first but condition on the second, while evaluator-validation methods estimate the second but stop short of the decision. Worse, buying more re-evaluation cannot settle the second: randomization governs which requests are scored, not how a score is produced, so the table stays uncertain however much evaluation is purchased. Yet the deployment decision may still be determined even when the table is not. We therefore ask whether one assignment stays optimal across every quality table consistent with the evidence. For the fixed-budget problem, this admits an exact two-solve certificate: solve once at the estimated table and once at a least-favourable table. Agreement certifies the assignment; disagreement identifies the model-workload pairs where further evidence can matter. We propose CASE (causal active sequential experimentation), which targets evaluation to those pairs and repeats the test as evidence accumulates. On a production log, the measurement failure is the larger of the two: correcting assignment exactly still leaves most of the loss, and randomized re-evaluation does not remove it. In our experiments, the available evidence often does not determine the assignment. On paid software tasks, better information about model quality yields more savings than further optimization of the assignment on the same estimates.

In resin transfer moulding, complete saturation of the fibre preform is necessary before the resin front reaches the outlet vent(s), to prevent dry-spot formation. In practice, the flow front rarely advances uniformly due to race-tracking effects. We propose a combined estimation and control strategy to address this issue. We use pressure-sensor data collected during filling to estimate the unknown race-tracking strengths via an iterated extended Kalman filter, and to simultaneously optimise auxiliary gate pressures to prevent the resin from arriving at the vent before complete saturation occurs. To make this approach feasible in real time, we replace the expensive finite element-control volume model with neural network surrogate models. The Bayesian approximation error framework is used to account for the discrepancy between the surrogates and the original model. To make the training of the surrogates feasible with time-dependent control actions, we prove that the flow-front geometry depends only on the time-averaged gate pressures. We demonstrate the methodology on a representative forked geometry, showing that the combined estimation-and-control framework can substantially reduce the number of unfilled nodes at the end of filling compared with an uncontrolled baseline. However, the level of improvement depends strongly on the location and number of auxiliary gates.

We study the design of linear time-invariant (LTI) encoder-decoder pairs for transmitting the state of a discrete-time LTI vector source over power-constrained parallel Gaussian channels with feedback. Two types of power constraints are considered. Under individual subchannel power constraints, a necessary and sufficient condition for designing an encoder-decoder pair that achieves bounded estimation error covariance (EEC) is established via two coupled majorization inequalities involving the subchannel signal-to-noise ratios and the antistable poles of the source. Under total channel power constraint, we derive the minimum total power required for a feasible encoder-decoder design by exploiting partial-order progamming under majorization order. An analytical optimal power allocation is obtained for the case of equal noise variances, which admits a water-filling interpretation; for general noise case, a sequential water-filling algorithm is developed. Our results reveal that the difficulty of transmitting a discrete-time LTI source via LTI coding is governed not only by its topological entropy, but also by the evenness of the log-magnitudes of its antistable poles. The design methods for feasible encoder-decoder pairs are also provided.

Diffusion models are increasingly used not only for sampling from learned data distributions, but also for generating samples that optimize task-specific objectives. A common approach is to guide the reverse diffusion process using gradients of an external objective. However, when the data distribution is supported on a structured feasible set, such as a manifold or a constraint set, gradient guidance can move samples away from the learned data geometry. In this paper, we study a simple projected-gradient-guided diffusion update based on the observation that the Stein denoising operator can act as an approximate projection onto the data geometry. The proposed update incorporates the objective gradient inside the denoising step, yielding an inference-time method that uses only a pretrained denoiser and gradient evaluations. We analyze this update as an inexact projected-gradient method for constrained optimization over learned feasible geometries. Our theory covers three settings: linear manifolds, compact convex feasible sets, and compact Riemannian submanifolds. In all these settings, we prove descent and finite-time convergence guarantees. Numerical experiments support the theoretical interpretation and illustrate how the proposed update balances objective descent with preservation of the learned geometry.

De Cock and De Moor conjectured that two matrices built from the solutions of three coupled Lyapunov equations always share their eigenvalues, an identity linking principal angles between model subspaces with the canonical correlations between the past and future of a stochastic process. The conjecture was recorded as Problem 9.1 of Unsolved Problems in Mathematical Systems and Control Theory. We prove it under the natural nonresonance condition, without stability or diagonalizability, and show that the two matrices are similar. The proof exposes a Cauchy-matrix structure created by the rank-one perturbation and reduces the problem to rational interpolation, and the main theorem has also been verified in the Lean~4 proof assistant. The same structure gives a normal form that depends only on the poles and zeros of the model. Off the stable set the eigenvalues become squared cosines of angles in an indefinite metric. We prove an inertia theorem for them and show that reflecting a pole or a zero across the unit circle acts on the angles by a principal pivot transform. For several inputs and outputs, where the conjecture fails, we identify the subspaces whose angles do give the canonical correlations. We also relate our approach to the independent proof of Gillberg and Löfberg.

This paper is devoted to developing a framework for stochastic growth models with environmental risk, in which rare but catastrophic shocks interact with capital accumulation and pollution. Building on the Poisson point process formulation studied in arXiv:2511.13568, we extend the model to disasters driven by a marked Hawkes process, allowing past disasters to temporarily increase the likelihood of subsequent shocks. Our work focuses on a subcritical Markovian Hawkes specification, in which the state space is augmented by the self-excitation component of disaster risk. We establish the well-posedness and nonexplosion of the resulting controlled Hawkes dynamics. Using the Hamilton-Jacobi-Bellman characterization of the corresponding Poisson control problem, we obtain quantitative estimates for the Hawkes excitation process and prove, under a small-excitation scaling, that the Hawkes value function converges to its Poisson counterpart as the magnitude of self-excitation vanishes. This provides a rigorous Poisson approximation of the stochastic control problem and quantifies the effect of self-excitation on optimal growth under environmental disaster risk.

This survey provides overview of distributed estimation, filtering, and fault detection techniques in the context of cyber-physical systems (CPS). To establish a strong foundation, we first define essential aspects of linear dynamical systems and related graph theoretic concepts, emphasizing observability conditions that are key for local state estimation. After discussing consensus algorithms, this survey highlights single-time and double-time-scale consensus-based estimation and filtering approaches. We provide a detailed comparative analysis of these methodologies, examining their computational requirements, communication overhead, and performance characteristics in resource-constrained environments. We further explore different diffusion-based estimation techniques and observationally redundant designs to enhance resilience and robustness against failures and adversarial attacks. In addition, we investigate distributed fault detection methods that enable local isolation of faults over large-scale CPS. We present both stateless and stateful detection mechanisms, along with threshold-based techniques that balance detection accuracy and false alarm rates. These approaches are essential for maintaining system integrity and preventing cascading failures in critical infrastructure. This survey concludes with an exploration of diverse real-world applications. We examine implementation challenges and algorithm adaptations in smart grid and power networks, social systems, target tracking and localization, and intelligent transportation systems. By bridging theoretical insights with practical applications, this survey and tutorial provides valuable understanding and research directions in the field of distributed algorithm design for CPS, offering both newcomers and experienced researchers a comprehensive resource for addressing current challenges and future opportunities.

The method of ellipcenters (ME) is a recent technique developed for unconstrained minimization. Its iteration relies only on first order information and consists of building a suitable two-dimensional ellipse that tries to capture intrinsic ill-conditioning of the problem. The center of the ellipse is taken as the next iterate, which justifies the name of the method. ME was already shown to converge linearly when the objective function is smooth and strongly convex. The special case when the objective is quadratic was studied in the first paper on ME and is also the subject of our work here. In this paper, we propose two variants of ME: RelaxME which adds in ME an additional relaxation step at each iteration and MomME which embeds momentum in ME. We prove linear convergence of RelaxME and MomME and, in particular, we show convergence of RelaxME and MomME (and also of ME) in one iteration when the matrix of the quadratic form has only two distinct eigenvalues. Finally, we provide the results of numerical experiments which compare on five optimization problems (and different combinations of parameters defining these problems) ME, RelaxME, and MomME, with 3 other optimizers: the conjugate gradient method [10], Barzilai and Borwein gradient method with long step [2], and the gradient method with adaptive spectral step length [7]. On most instances, MomME provides the smallest number of iterations and conjugate gradient and MomME provide the smallest CPU times and similar CPU times. This opens optimistic possibilities for ME with momentum in broader settings.

Physics-informed neural networks (PINNs) often face ill-conditioned objectives that limit high-accuracy training. Dense quasi-Newton methods improve local conditioning but require expensive optimizer state, while Kronecker-factored methods such as SOAP scale to larger networks but rely on periodic basis updates. We introduce \method, which augments SOAP-style preconditioning with a scalar secant-energy correction adapted to Kronecker geometry and an adaptive basis update followed by variance-state downscaling. We characterize the directional secant matching induced by the scalar correction and give a bound on variance-state mismatch across basis changes. Across eight PDE benchmarks, \method attains the lowest final residual on six, including Burgers and Boussinesq, while SOAP-family baselines perform better on Gray-Scott and Ginzburg-Landau. On Boussinesq, \method reaches a residual of $10^{-5}$ in 4.1 hours with 9.2 GB peak VRAM, while Adam does not reach this target within 14 hours. Three-seed $L^2$ and $H^1$ errors on four representative PDEs support the link between lower residuals and improved solution accuracy. These results position \method as a scalable option for stiff, high-accuracy physics-informed training, rather than a uniform replacement for existing optimizers.

ISO New England's (ISO-NE) Day-Ahead Ancillary Services Initiative settles reserve products as financial call options on real-time energy prices. The system-wide strike price creates an efficiency-reliability tradeoff: increasing it lowers competitive reserve offers, but weakens resources' incentives to incur preparation costs and remain available for real-time performance. The existing strike price rule does not explicitly account for heterogeneous resource incentives and reserve requirements. We develop an optimization framework that selects the highest strike price while ensuring that enough resources retain an incentive to prepare and collectively satisfy the reserve requirements. Because a resource's preparation decision may affect the resulting real-time price distribution, its incentive depends on an unobservable counterfactual. To address this, we derive a tight lower-bound certificate using only the available conditional price distribution and a bound on the resource's price impact. We show that each resource enters the optimization through a single incentive threshold and that any finite optimal strike price occurs at one of these thresholds. This yields a tractable exact solution method based on threshold calculations and a small number of linear feasibility checks. Using reconstructed ISO-NE conditional price distributions and representative gas-fired resources, we find that higher heat-rate combustion turbines are more likely than combined-cycle resources to constrain the strike price choice.