Papers

Sensor placement for maximizing the estimation performance of the Kalman filter is an NP-hard optimization problem. Furthermore, its feasible set grows combinatorially with the candidate locations and the number of sensors. In this paper, we study this sensor placement problem for a 3D thermoelastic system modelled as a discrete-time linear stochastic model. We use the Novel Binary Artificial Bee Colony (NBABC) algorithm with a Gramian-based pre-filter to reduce the computational complexity. Our results show the efficiency and the fast convergence of the proposed approach.

Understanding how information spreads and opinions evolve on social media is a core challenge in computational social science. Users constantly face competing topics, yet their decisions to engage are shaped by social learning, perceived utility, and cognitive limits. Traditional models often separate content from behavior, missing how individual cognition and social interaction jointly drive large-scale discourse. We propose a language-independent computational framework that bridges semantic topic modeling with evolutionary game theory and agent-based simulation. Using BERTopic, we extract coherent topics from a large Weibo dataset. We then quantify engagement through a unified metric based on likes, comments, and reposts. In NetLogo, agents update topic preferences via local imitation, guided by payoff comparisons and behavioral noise—mirroring real-world bounded rationality. Tests on two real-world datasets show that our model successfully replicates observed topic diffusion trends. It highlights how social learning frequency and payoff sensitivity shape public attention. Our results demonstrate that micro-level mechanisms—imitation and noise-tolerant choice—can produce emergent macro-level patterns. This work contributes to human-computer interaction by linking semantic analysis with behavioral simulation, offering insights into the cognitive and social foundations of online collective behavior. The framework also has practical potential for misinformation resilience, opinion forecasting, and adaptive content curation.

Planning accessible public services such as health care, emergency response, and schools often requires not only choosing where to open facilities but also improving the network that connects people to them, for example upgrading flood-prone roads in vulnerable regions. Most location models, however, take the network as fixed and the budget as given. We study the Maximum Covering Network Design Problem, in which a single budget is shared between opening facilities and upgrading weak links to maximize the population within a target travel distance of an open facility. The problem is hard even on the simplest networks, and planners usually want to see how coverage grows with the budget, not a single plan. We develop an exact dynamic-programming framework that exploits a property common to real road networks: their low connectivity, with many cut points whose removal disconnects the network. On trees, the recursion is self-contained: each state reduces to a few simple facility and upgrade choices that are fast to compute without a solver, giving predictable running times; for larger budgets and travel distances it outperforms solving the MILP formulation directly. On general low-connectivity networks, the framework decomposes the problem at the cut points and embeds a given MILP formulation to solve the resulting pieces, coordinating them through coverage conditions at the interfaces. This lets us compare a formulation on its own against the same formulation inside the framework: across 306 test cases the framework matches or outperforms direct solving on more than 80% of instances. Because it evaluates all budget levels in a single run, it also yields the full coverage-versus-budget curve at no extra cost, whereas direct solving must split its time across individual budgets.

We study whole-sequence convergence of the smoothing-based full-splitting proximal subgradient method (S-FSPS) for structured nonconvex and nonsmooth fractional programs, introduced by Boţ, Li, and Tao (SIAM J. Optim., 35(4):2623–2653, 2025) as Algorithm~4.1. Existing theory guarantees only the existence of a subsequence converging to a limiting lifted stationary point. We show that this guarantee is sharp by constructing two admissible instances whose corresponding primal sequences both have cluster set $\{1\}\times\mathbb S^1$ and infinite length, although every cluster point is a limiting lifted stationary point. The construction prescribes a slowly rotating spiral and realizes it exactly through a compatible first-order jet and a $C^{1,1}$ Whitney extension. In the first instance, $A$ has rank one and every smoothing-dual iterate is nonzero. In the second, the feasible set is full-dimensional, $A$ has full row rank, and each of $f\circ K$, $g\circ A$, and the numerator $g\circ A+h$ is nonconstant on the feasible set. The first instance also yields a nonconvergent example for the corresponding variable-smoothing, single-loop, full-splitting method for nonconvex and nonsmooth composite optimization, although that method still admits a subsequence converging to an exact stationary point. Thus, a vanishing but nonsummable smoothing schedule does not imply whole-sequence convergence.

We study infinite-horizon time-inconsistent Markov decision processes with a countably infinite state space and unbounded reward functions. The reward is allowed to depend explicitly on the initial time and initial state, thereby accommodating general sources of time inconsistency. We seek relaxed feedback equilibria, and our approach is based on entropy regularization and weighted functional analytic methods. With entropy regularization, we characterize a regular relaxed equilibrium through a fixed-point operator. By introducing two weight functions with distinct roles, one controlling the growth of rewards and values and the other defining the ambient weighted space, we construct a compact invariant set under a product topology and apply the Schauder-Tychonoff fixed-point theorem to establish existence of regularized equilibria. Importantly, the invariant set can be chosen uniformly for small entropy weight $\lambda\in(0,1]$. We then let $\lambda\to0+$ and show, through compactness, concentration of Gibbs policies, and uniform-integrability arguments, that a subsequential limit is a relaxed equilibrium of the original unregularized problem. We further study a policy iteration algorithm (PIA) for the entropy-regularized equilibrium problem. Under a weighted-discounting structure and sufficiently strong discounting, we establish exponential convergence and uniqueness of the regularized equilibrium in a suitable weighted Banach space. Combining the policy-iteration error with a quantitative soft-max approximation bound, we show that the iterated policies constitute weighted $\varepsilon$-equilibria for the original unregularized problem and derive an explicit regret estimate. A numerical example illustrating the convergence of PIA under strong discounting and a counterexample demonstrating its failure under weak discounting are also provided.

Transmission system operators often reconcile market-cleared DC dispatches with AC physics through power-flow solves (ACPF), yet the resulting setpoints can still violate voltage (Volt) and reactive-power (VAR) limits. Maintaining secure voltage profiles and adequate VAR support therefore requires fast corrective decisions that are implementable in operation. This paper presents a novel homotopy-based continuation method for discrete-control Volt/VAR Optimization (VVO) that coordinates switchable devices, such as on-load tap-changing transformers (OLTCs) and capacitor banks (CBs). Experiments on IEEE, PEGASE, and RTE systems show that the proposed VVO produces AC-feasible setpoints within practical runtime, while reducing voltage deviation, VAR dispatch, and generation cost. VVO also achieves comparable performance using ACPF-adjusted DC dispatches as inputs relative to AC-feasible dispatches, indicating that it can be integrated naturally into existing transmission dispatch practices to strengthen grid operation.

Transport resilience work is often split across separate data preparation scripts, network models, simulation tools, image inspection systems and reports. This fragmentation makes it difficult to move from an observation to a tested and reviewable decision. We introduce ResiliFlow, an open transport world model concept and an implemented platform for infrastructure resilience, response and recovery. The platform connects two workspaces. Disaster Transport Resilience Analysis provides six map-centred functions for critical-road and critical-area identification, recovery prioritisation, disruption routing, resilience testing and scenario simulation. AI-based Transport Infrastructure Perception and Decision Support organises street-level and satellite evidence, detects visible road, footpath and kerb conditions, and prepares these observations for human-reviewed intervention planning. Both workspaces share an eight-step cycle of perception, prediction, model development, verification, execution, decision, feedback and memory. Research Validation records assumptions and checks, while a local Assistant and an optional multi-provider large language model Copilot translate user questions into bounded calls to executable tools. We document the platform architecture, representative mathematical models, interface evidence and computer-vision learning results. Examples show accurate recognition across eight visible-condition classes, while compact error analysis demonstrates how difficult cases guide continued learning. ResiliFlow shows how transport models can become an inspectable, reusable and question-led system rather than a collection of disconnected analyses. The accompanying release is intended to support research collaboration, public scrutiny and extension under institutional review.

Surface hopping is an attractive mobility mode for small-body exploration, but designing fuel-optimal hops on asteroid 433~Eros requires solving a nonconvex optimal control problem with an irregular polyhedral gravity field, thrust–mass coupling, and collision-avoidance constraints. We show that a physics-informed Bayesian Optimization (BO) warm-start—a Gaussian-process search over a single Bézier control point that requires no offline training—provides a more reliable initialization for Sequential Convex Programming (SCP) than the standard straight-line guess. The straight chord penetrates the asteroid on every inter-site transfer considered here and degrades convergence. The physics-informed BO reference feeds an SCP stage in which a log-mass change of variables convexifies the thrust–mass coupling and nearest-facet half-spaces enforce collision avoidance, and an automated Pareto time-of-flight sweep selects fuel-priority solutions without introducing bilinear terms. Applied to all 20 ordered transfers among five representative surface sites and validated under 10 random seeds, the framework tracks every trajectory to meter-level terminal accuracy in closed-loop Monte Carlo simulation, completes a five-site tour for one fifth of the propellant budget, and reduces mean $\Delta V$ by roughly one third relative to an idealized two-impulse ballistic trajectory estimate. A straight-line ablation credits the warm-start with cutting the mean SCP iteration count from 8.8 to 5.9 and removing the one convergence failure. A target-perturbation analysis further shows that the solutions vary smoothly with the landing target, with no jumps between local basins.

We explore a new growth condition for Lipschitz functions around local minimizers, recently proposed in the context of Goldstein-subgradient-based algorithms and their behavior in practice. On generic examples, these algorithms are often observed to converge approximately linearly. We focus on objectives that are piecewise twice continuously differentiable. In that case, the new growth condition holds when the objective is, in addition, strongly convex. In the nonconvex case, we prove that quadratic growth in conjunction with a regularity property for the active gradients suffices. Computational experiments illustrate the importance of the assumptions.

The edge-of-stability (EoS) phenomenon of full-batch Adam has been widely observed, yet its underlying dynamical mechanism remains poorly understood. In this paper, we identify Adam's second-moment adaptation as a negative-feedback mechanism that drives the dynamics toward the stability boundary. We characterize this mechanism through the *active curvature*, namely, the preconditioned curvature along the preconditioned gradient direction, and establish rigorous characterizations in progressively richer settings: rank-one quadratics with momentum, diagonal quadratics, on which the active curvature separates from the sharpness, and general objectives. Importantly, the mechanism predicts *gradient reversal* of full-batch Adam near the edge: consecutive gradients repeatedly point in nearly opposite directions, as we observe across fully connected networks, ResNets, ViTs, LSTMs, GPT-2 medium, and Adam-family optimizers. Consistent with this picture, averaging iterates suppresses these fast oscillations and produces smoother and lower loss curves. Together, these results provide an important first step towards fully understanding the dynamical behavior of Adam's EoS through active curvature and gradient reversal.

Transformational electric vertical take-off and landing (eVTOL) vehicles have gained significant attention over the past decade due to their efficient wing-borne cruise capabilities and reduced reliance on ground-based infrastructure. However, control system design for these vehicles remains challenging, as they must operate across multiple flight phases, each with distinct dominant dynamics. If left unaddressed, this complexity would significantly increase pilot workload, thus motivating the development of pilot control systems for multi-phase flight operations. The Simplified Vehicle Operations concept presents a promising strategy for reducing pilot workload. This study presents the design and implementation of a novel pilot control concept for eVTOL aircraft, validated through a tandem tilt-wing aircraft simulation on a full-motion simulator equipped with an active, force-feedback side stick. The system provides pilots with tactile feedback during specific flight phases, supporting intuitive control. The proposed approach enables seamless transitions and multi-phase flight maneuvers by leveraging the available degrees of freedom. Furthermore, an optimal-control-based methodology is proposed as a metric to evaluate command-filter-induced performance penalties and inceptor activities. The results show that the proposed command filter does not significantly increase the mission duration compared to the closed-loop system, while the active side stick helps reduce inceptor activity.

Variable active power injections arising from device behavior or compromised dispatch complicate voltage regulation in electric power networks with distributed energy resources (DERs). An operator can limit the resulting voltage deviations by remotely selecting DER reactive power parameters before observing the active power injections. IEEE Standard 1547-2018 specifies constant power factor as one such control mode, coupling each device's reactive power to its realized active power. Using a linear voltage model, we formulate the operator's decision as a robust minimax problem in which the operator minimizes the largest feasible aggregate voltage deviation. We solve this problem by expressing the power factor decisions through continuous reactive to active power ratios and exactly decomposing the payoff according to the signs of the voltage deviations. When every feasible voltage residual remains on its initial side of nominal, the resulting ratios cancel each injection's contribution and yield a closed form minimax strategy. We identify realistic DER ratings for which this strategy applies and quantify the regulation capacity lost under restricted power factor ranges. Numerical tests check the cancellation computation, solve the complete minimax problem directly at a representative DER rating, and compare the linear voltage predictions with nonlinear AC power flow.

Directional subdifferentials of the value function provide a quantitative measure of optimal value response to perturbations. While existing results are largely limited to finite-dimensional settings, this paper develops a comprehensive variational framework in Asplund spaces. We establish essential directional calculus rules, extending directional nonsmooth analysis to infinite dimensions. To address the lack of compactness of bounded sets in infinite-dimensional spaces, we introduce a new directional condition, under which we derive upper estimates for directional limiting and singular subdifferentials of the value function. These results provide a refined analytical foundation for sensitivity analysis in infinite-dimensional hierarchical systems.

A central methodological question in data-driven control is whether to adopt a direct or indirect approach. Direct methods infer a controller or certificate directly from data, while indirect methods first identify a system model and then apply model-based control techniques. Recent developments of the direct method have led to finite-sample guarantees for the data-driven stability analysis of switched linear systems under various settings. However, for the indirect method, such guarantees remain largely elusive. In this paper, we provide a novel framework for the stability analysis of switched linear systems from noisy state measurements, using the indirect approach and quadratic Lyapunov analysis. Our framework comes with finite-sample guarantees on the convergence rate of the system. For that, we combine generalization bounds from machine learning and system identification with sensitivity analysis from quadratic Lyapunov analysis. To enable comparison, we also extend existing direct data-driven methods to handle measurement noise beyond the bounded noise case currently available in the literature. Finally, we compare the two approaches through numerical experiments, revealing that under moderate-to-high noise levels the indirect approach yields tighter probabilistic guarantees as well as greater robustness to noise and outliers than the direct approach

We study continuous-time dynamic portfolio optimization under a Conditional Value-at-Risk (CVaR) constraint on the investor's terminal loss. For a general class of convex trading objectives, we exploit the auxiliary-threshold representation of CVaR to establish the existence of an optimal strategy and strong duality without requiring market completeness. These results motivate a dual-based nested bisection–golden-search algorithm over the threshold and Lagrangian multiplier, where the inner iterations reduce to standard unconstrained stochastic control problems. We prove that the resulting strategies converge to the optimal control as the number of iterations tends to infinity. Numerical experiments recover the Merton policy when the risk constraint is nonbinding. When the constraint is binding, the optimal strategy becomes state dependent: the investor reduces risky exposure following adverse outcomes but preserves, and near maturity may increase, exposure following favorable outcomes. Thus, a terminal CVaR constraint produces an asymmetric reallocation across states rather than uniform de-risking. Nontraded endowment risk amplifies the conservative adjustment, whereas price impact lowers desired positions and adjustment speeds.

This paper addresses the problem of estimating upper bounds on the probability that a dynamical system will enter an undesirable region at some point within a finite time horizon. The primary source of uncertainty lies in the system's initial state, for which only a finite set of moments is known or within a prescribed interval. To tackle this problem, we formulate a measure-based program and propose its relaxation using the moment-sum-of-squares (moment-SOS) framework. The corresponding dual problem is introduced as a functional program, which is subsequently strengthened into a sum-of-squares (SOS) program. Notably, this dual formulation bears a structural resemblance to classical barrier function techniques for certifying system safety, with the key distinction that it yields a probabilistic certificate. The effectiveness of the proposed approach is demonstrated through multiple case studies, including a case involving an object in orbit.

This article develops a self-contained Lie-theoretic route from linear controllability to nonlinear controllability on matrix Lie groups. The organizing question is whether local algebraic information can be propagated into statements about reachable sets. The linear case supplies the model: the matrix exponential, Cayley-Hamilton theorem, trajectory formula and Kalman family B,AB,...,An-1B reduce controllability to finite-dimensional linear algebra. In the nonlinear setting, Lie brackets replace matrix powers, but the associated Lie algebra may be infinite dimensional and the finite-dimensional Lie correspondence can fail. Particular emphasis is placed on rotation groups. Skew-symmetric matrices, their exponentials, commutators, one-parameter subgroups, and the Baker-Campbell-Hausdorff formula provide a concrete laboratory for seeing how infinitesimal directions propagate on SO(n). A numerical SO(3) simulation illustrates the geometry of controlled rotations, while explicit SO(4) and SO(7) commutator sequences make the propagation of a localized control direction visible. The article then develops the attainable-subgroup argument for right-invariant systems, gives a detailed proof sequence behind the Yamabe step, and works through solvable, nilpotent and ideal examples for upper-triangular matrix algebras. The finite-dimensional mechanism is finally contrasted with Sussmann's local controllability theory for general nonlinear systems.

The term "dual control" refers to the dual objective of simultaneously balancing exploration and exploitation. Problems of this kind have been studied for nearly a century. This paper is devoted to theory and methodology relevant for optimal control of linear time-invariant systems whose parameters are initially unknown and must be learned by active probing. We review the main ideas underlying four major research directions: Multi-armed bandits, self-tuning regulators, regret rate minimizing controllers, and minimax optimal dual controllers. The first three have a long history and rich literature, whereas the fourth provides a promising framework for robust dual control.

We study bilateral teleoperation between nonlinear, multi-DOF robotic manipulators in the presence of constant communication delays. Unlike classical wave-transformation architectures that transmit a coordinating force, we consider the case where the environmental force is reflected to the master side to enhance teleoperation transparency. Since direct contact force feedback might destabilize the closed-loop system, we first develop a passivity-shortage characterization for the Euler–Lagrange remote system using a linear matrix inequality (LMI) approach. An upper strictly passive communication law is then employed to compensate for the computed passivity shortage so that the closed-loop stability under delays as well as position and force synchronization are preserved under appropriate conditions. Simulations with nonlinear 2-DOF robotic manipulators in different settings illustrate our approach.

We address the practical computation of feedforward steering inputs for a car with n trailers via differential flatness. The standard route (iterated symbolic differentiation of the flat output) scales prohibitively with n: even with computer-algebra software the expression sizes grow super-exponentially and become intractable beyond n approx. 5. We propose an algorithm that combines four ingredients (angular intermediate variables, factorisation of the recursion in submaps, rescaled higher-order product/quotient rules, and a composition rule based on truncated formal power series instead of Faa di Bruno's formula). We benchmark the proposed method against (i) direct symbolic differentiation in SymPy and (ii) Faa di Bruno's formula evaluated via Bell polynomials. Both reference methods hit a clear computational wall: SymPy reaches a 20 s timeout at derivative order r = 14, while the Bell-polynomial recursion exceeds a 60 s timeout beyond r = 24. The proposed approach has O(r3) arithmetic complexity in the derivative order and remains under one millisecond up to r = 40, with numerical agreement to machine precision in the regime where the reference methods succeed. As an end-to-end illustration, a 20-trailer parking manoeuvre is computed and animated.

We introduce a model with control vacations instead of standard queueing control systems with permanent control. The researched model is an M/M/1 queue with temporary periods of service rate control with two available service rates. After a control period of exponentially distributed length, a control vacation is initiated during which a fixed service rate $\mu$ is used. The start of the next control period needs to be scheduled directly at a certain cost. We will use the Markov Decision Process from Kanavetas et al. arXiv:2605.31573 to find a sufficient condition that ensures that the average expected cost can be reduced w.r.t. the model that only uses the fixed service rate. Under this condition we will use properties of this related process to construct a cost reducing policy. The process with control vacations under specific policies induces a renewal reward process. We use a Tauberian theorem to relate the average expected cost of this renewal reward process to a vanishing discount method and analytically determine a lower bound of the average expected cost reduction. Finally, we study the actual attained average cost reduction for these policies through simulation.

We study a shape optimization problem among convex bodies in $\mathbb{R}^n$ that minimize or maximize weighted perimeters of the form $\int_{\partial\Omega} \phi(|x|) \, \mathrm{d} H^{n-1}(x)$ under a standard perimeter constraint. We prove the existence of extremals for general weight functions in any dimension. In dimension two, we prove that the degenerate needle configuration $(-a,a)\times \{0\} \subset \mathbb{R}^2$ is the optimizer for a wide family of weights, including $|x|^p$ for $p \in (0,2]$ and $|x|^{-\alpha}$ for $\alpha \in (0,1)$, among convex curves satisfying a symmetry assumption.

Augmented Lagrangian methods are effective for nonlinear equality-constrained optimization, but solving their nonlinear primal subproblems can be expensive. For smooth nonconvex problems with deterministic or stochastic objectives, we propose a nonlinear-residual linearized augmented Lagrangian method (NR-LALM) that replaces this subproblem by a regularized Gauss-Newton-type step while retaining the classical multiplier update based on the nonlinear constraint residual. The resulting step is computed from one symmetric positive-definite linear system, but the mismatch between the linearized primal model and the nonlinear-residual update produces a quadratic constraint-linearization error in the multiplier identity. We show that this error can be controlled under local regularity; multiplier boundedness and trajectory localization are derived rather than assumed. With fixed, accuracy-independent parameters, deterministic NR-LALM finds an $\varepsilon$-approximate Karush-Kuhn-Tucker (KKT) pair in $O(\varepsilon^{-2})$ iterations and first-order oracle evaluations. For stochastic objectives, a projected stochastic path-integrated differential estimator with safeguarded restarts requires, in expectation, $O(\varepsilon^{-3})$ stochastic-gradient evaluations and $O(\varepsilon^{-2})$ constraint and Jacobian evaluations. Compactness and a Kurdyka-Lojasiewicz condition further yield finite-length convergence of the deterministic primal-dual sequence. An optional minimum-norm second-order correction reduces the constraint-linearization error from second to fourth order without changing the complexity orders. All theoretical results are formalized in Lean 4. Numerical experiments confirm the predicted error orders and show favorable performance on high-dimensional deterministic and stochastic problems.

A minibatch can influence training beyond the update at which it is observed because AdamW stores past gradient information in its optimizer states. We study this delayed effect through paired trajectories that differ only in one gradient update and share the same subsequent training sequence. We formulate AdamW as a finite-horizon input–state–output (ISO) system whose state contains the model parameters and first- and second-moment estimates. Linearizing the joint dynamics yields a signed response operator that maps a localized gradient perturbation to its future loss effects, revealing how optimizer memory shapes their magnitude, timing, and sign. We further derive an exact multistep error decomposition and establish first-order finite-horizon accuracy under local smoothness and controlled activation switching. Experiments validate the response mechanism and optimizer-state effects, while repeated-future analyses reveal substantial prospective structure in delayed influence that can be partially recovered from ISO approximations. Code is available at https://github.com/Kanyooo/Loss_ISO.

This paper proposes a controller design method for shaping the controllability Gramian into a desired form to design the effect from exogenous inputs to the system state. Using the Bures–Wasserstein distance, we formulate the shaping problem as the minimization of the distance between the system Gramian and a desired Gramian, and the objective function is shown to be strictly convex on the set of symmetric positive definite matrices. In addition, by deriving a semidefinite programming formulation via a linear matrix inequality (LMI), computational efficiency is improved and additional LMI constraints can be incorporated. When the exogenous input is modeled as Gaussian white noise, the proposed framework is closely related to $H_2$ control, which can be interpreted as a special case of optimal transport. Numerical examples demonstrate anisotropic controllability design for a guidance robot and verify the ability to impose additional directional constraints through LMIs. The numerical examples also confirm that the proposed method approaches $H_2$ control as the desired Gramian tends to zero.

Meissner polyhedra are constant-width bodies obtained from extremal finite sets of unit diameter. Such a generating set may contain dangling points, namely points having exactly two diametric neighbors. This article studies whether these points can play an essential role in surface-area minimization. Given an extremal set we show that the smallest surface area among the Meissner polyhedra based on it cannot increase by deleting a dangling point. Adding a dangling point cannot decrease the smallest achievable surface area. This reduces the search for area-minimizing Meissner polyhedra to generating sets without dangling points.

High-multiplicity flexible job shops involve many copies of a small set of job types that must be scheduled on alternative machines. Fluid relaxations provide scalable workload lower bounds, but their fractional machine allocations do not define feasible schedules for individual jobs. We show that, after a suitable finite scaling, an optimal fluid allocation can be realized exactly by a feasible repeating discrete schedule. The construction scales the fluid allocation to integer operation counts, places the resulting operations in nonoverlapping machine intervals, repeats this arrangement, and links operations across repetitions into individual jobs without moving any interval, thereby enforcing job precedence while preserving machine feasibility. For growing finite instances with the same job-type composition, even with a fixed number of extra jobs, the gap between the optimal makespan and the fluid lower bound remains bounded by a constant; hence the relative gap vanishes as the instance grows. Guided by this repeated structure, we develop type-based cyclic template replay (TCTR), which searches job-type templates using an optimization model whose size does not grow with the number of job copies and replays the selected template on the full instance. On 676 multiplicity-expanded public flexible-job-shop instances, TCTR is feasible in every case and achieves a 1.54% mean gap to the fluid lower bound, compared with 5.32% for a job-indexed adaptive large-neighborhood search and 6.18% for a hybrid genetic algorithm.

Rather than prescribing an evaluation interval a priori, the proposed framework characterizes each evolving unsteady flow using a sequence of time windows. A consecutive-window convergence criterion is introduced to automatically identify a representative time window within its fully developed stage. The objective evaluation and discrete adjoint analysis are then carried out consistently over the identified representative time window. The framework is implemented using a regularized lattice Boltzmann method-based large-eddy simulation (LBM-LES) solver together with a partial bounce-back fluid-solid model. The consecutive-window convergence criterion is first validated using the backward-facing step flow. Cylinder-flow applications are then employed to investigate the influence of different flow regimes on the proposed framework. The wake-flow recovery problem verifies its effectiveness for unsteady topology optimization, while U-bend optimization further demonstrates its capability to identify and reorganize complex vortical structures.

We establish marginal and functional convex order comparisons for graphon mean-field systems on $\mathbb{R}^d$, including the infinite-horizon setting. A key difficulty is that convex order cannot in general be transferred through the usual particle approximation, which requires us to work directly with Euler schemes for the graphon mean-field system. Under a suitable dissipativity condition, we establish Euler approximation estimates that are uniform in both time and the agent label, and combine them with forward-backward induction arguments to obtain the convex order comparisons. For the infinite-horizon problem, dissipativity provides the required uniform-in-time stability, while an exponentially weighted $L^2$-space enables trajectory-level convergence and leads to the functional convex order on $[0,\infty)$. As an application, we derive value-function comparisons for a class of one-dimensional linear-quadratic graphon mean-field games.

In this paper, we study the structure of the value function in constrained infinite-time optimal control (CITOC) problems of piecewise affine (PWA) systems, with $\ell_1$ or $\ell_\infty$ stage cost. Existing works, such as [1], establish that the resulting value function is PWA in the state. However, existing results do not analyze whether the value function is a proper PWA function, i.e., with a finite number of affine pieces over compact sets, or whether the number of pieces can be infinite. We show that the latter case is indeed possible by means of an explicit example, which is also instrumental in establishing rigorous and easily verifiable sufficient conditions that ensure that the resulting value function is a proper PWA function. Our theoretical findings complement well-known results, e.g., the linear-quadratic case, and serve as support for recent learning-based control schemes for PWA systems. Throughout the paper, the proposed results are illustrated by means of a numerical example.