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math.OC: explore 248 source-linked works published from 2017 to 2026, with original documents and citations.

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Includes records with this source-supplied label or an explicit phrase match in their metadata. Matches indicate a mention, not proof that a paper uses a method or tests a material. Source versions are consolidated by DOI.

Sources: arxiv. Collection updated 2026-09-16. Counts describe this index, not the complete source archives.

arXiv2026

Linear Coding of LTI Sources Over Vector Gaussian Channels: A Majorization Approach

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.

cs.IT↗
arXiv2026

Which LLM for Which Work? Budgeted Model Allocation under Uncertain Evaluation

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.

cs.LG↗
arXiv2026

Reciprocal-Manifold Annealed KKT Flows for Constrained Optimization: Application to the Nonconvex AC Optimal Power Flow

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.

math.OC↗
arXiv2026

Transformer-Based Flow Shop Scheduling Using MILP-Generated Training Data

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.

math.OC↗
arXiv2026

Successive design of backstepping observers for parabolic PDE-ODE systems and its duality to state feedback stabilization

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.

math.OC↗
arXiv2026

A Unified Perspective on Conformal Prediction and Wasserstein Distributionally Robust Optimization for Uncertainty Quantification

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.

math.OC↗
arXiv2026

Quiver Semistability and Structured Kalman Decompositions for Networked Linear Dynamical Systems

We introduce new notions of controllability and observability for networked linear time-invariant (LTI) systems based on $σ$-semistability of quiver representations. Utilizing King's criterion for $σ$-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 $σ$-semistability of representations of acyclic quivers with self-loops if the weight $σ$ has the same sign for all vertices with self-loops. Such quiver representations and weights arise from networked LTI systems.

math.OC↗
arXiv2026

Finite Sample Identification of Analytic Nonlinear Systems

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.

eess.SY↗
arXiv2026

On the suboptimality of stochastic MPC with varying constraint horizon

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.

math.OC↗
arXiv2026

A note on the $Σ_2^P$-completeness of the Frobenius number

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 $Σ_2^P$-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).

cs.CC↗
arXiv2026

Equilibria in Network Constrained Markets with System Operator

We study a networked economic system composed of $n$ producers supplying a single homogeneous good to a number of geographically separated markets and of a centralized authority, called the market maker. Producers compete à la Cournot, by choosing the quantities of good to supply to each market they have access to in order to maximize their profit. Every market is characterized by its inverse demand functions returning the unit price of the considered good as a function of the total available quantity. Markets are interconnected by a dispatch network through which quantities of the considered good can flow within finite capacity constraints and possibly satisfying additional linear physical constraints. Such flows are determined by the action of a system operator, who aims at maximizing a designated welfare function. We model such competition as a strategic game with $n+1$ players: the producers and the system operator. For this game, we first establish the existence of pure-strategy Nash equilibria under standard concavity assumptions. We then identify sufficient conditions for the game to be exact potential with an essentially unique Nash equilibrium. Next, we present a general result that connects the optimal action of the system operator with the capacity constraints imposed on the network. For the commonly used Walrasian welfare, our finding proves a connection between capacity bottlenecks in the market network and the emergence of price differences between markets separated by saturated lines. This phenomenon is frequently observed in real-world scenarios, for instance in power networks. Finally, we validate the model with data from the Italian day-ahead electricity market.

cs.GT↗
arXiv2026

Aspiration-based Perturbed Learning Automata in Weakly-Acyclic Games with Noisy Utility Measurements

Reinforcement-based learning dynamics may exhibit several limitations when applied in a distributed setup. In (repeatedly-played) multi-player/action strategic-form games, and when each player applies an independent copy of the learning dynamics, convergence to (usually desirable) pure Nash equilibria cannot be guaranteed. Prior work has only focused on a small class of games, namely potential and coordination games. Furthermore, strong convergence guarantees (i.e., almost sure convergence or weak convergence) are mostly restricted to two-player games. To address this main limitation of reinforcement-based learning in repeatedly-played strategic-form games, this paper introduces a novel payoff-based learning scheme for distributed optimization in multi-player/action strategic-form games. We present an extension of perturbed learning automata (PLA), namely aspiration-based perturbed learning automata (APLA), in which each player's probability distribution for selecting actions is reinforced both by repeated selection and an aspiration factor that captures the player's satisfaction level. We provide a stochastic stability analysis of APLA in multi-player positive-utility weakly-acyclic games under the presence of noisy observations. We provide conditions under which convergence is attained (in weak sense) to the set of pure Nash equilibria. A methodology is also derived for calculating the stochastically stable equilibria through the aspiration action functional minimization, which simplifies the derivation of stochastically stable states. Conditions can then be derived for convergence to the Pareto efficient Nash equilibria. To the best of our knowledge, this is the first reinforcement-based learning scheme that provides global convergence guarantees in weakly-acyclic games and in a fully-distributed setup. A Monte-Carlo simulation study validates the derived conclusions.

cs.GT↗
arXiv2026

Tensor-Based Reduced-Order Modeling for Optimization-Based Inverse Problems

We develop a tensor reduced-order modeling (TROM) framework for optimization-based inverse problems governed by parameter-dependent dynamical systems. The approach approximates the parameter-to-observation map directly in tensor-train (TT) format using TT-SVD or TT-Cross and integrates it into a regularized nonlinear least-squares formulation. Beyond accelerating forward evaluations, the low-rank tensor structure reformulates the inverse problem in reduced coordinates, assembles Gauss--Newton quantities without forming the full observation-space Jacobian, and minimizes the TROM objective over the discrete parameter grid. This tensor optimization provides either a stand-alone approximate solution or a data-informed initialization for a subsequent Gauss--Newton solve. We study an inverse heat-transfer problem in a heterogeneous medium, where the parameters describe the locations and radii of low-conductivity inclusions, and a FitzHugh--Nagumo parameter-estimation problem with a highly nonconvex landscape. Numerical experiments assess reduced-order model error, measurement noise, regularization, initialization, spatial discretization, and increasing parameter dimension. The results show that TROM reproduces full-order inversion at substantially reduced online cost. They also demonstrate that reduced-coordinate inversion, tensor-based optimization, and appropriate regularization improve robustness in higher-dimensional, noisy, and strongly nonconvex regimes. For the continuous TROM inverse problem, we develop an error-to-inversion analysis. Under local strong convexity of the regularized FOM objective and parametric smoothness of the FOM observation map, the error between the parameters recovered with the full-order model and TROM is bounded by controlled uniform errors in the surrogate map and its Jacobian, together with local FOM and curvature quantities.

math.NA↗
arXiv2026

Fast Trainable Multilinear Bases for Image Compression

The Discrete Fourier Transform (DFT), the Discrete Cosine Transform (DCT), and their block-wise variants underpin most deployed image and video codecs. Their effectiveness rests on three properties: their runtime is near-linear (up to a polylogarithmic factor) in the image size, they are exactly invertible, and they carry few to no parameters. We generalize these transforms to dataset-adaptive isometric multilinear bases that keep all three properties at the cost of a polylogarithmic number of parameters, by parameterizing each basis as an isometric tensor network, inspired by quantum many-body theory, and training one shared basis per image dataset with Riemannian optimization. Because the family contains the DFT and the DCT-IV (a variant of the DCT) as exact points, training can start from these transforms, and it improves on its starting point at the compression level it is trained for. We evaluate the bases on natural photographs and line drawings. On photographs, which the cosine basis already fits well, the best trained basis leads the DCT only under aggressive truncation. On Quick Draw line drawings, under a common codec at matched quality, the best trained basis stores each image in about 20% fewer bytes than the 8x8 block cosine transform of the Joint Photographic Experts Group (JPEG) format, not counting the one-off storage of the basis.

eess.IV↗
arXiv2026

Column Number of Delta-modular matrices: Refined Analysis via Sauer Matrices

In this paper, we build upon the analysis initiated by Gennadiy Averkov and Matthias Schymura (2022) and establish that the number of distinct columns of a $Δ$-modular matrix $A \in \mathbb{Z}^{m \times n}$ of rank $m$ is $O(m^3 Δ)$. This upper bound was previously known only for odd values of $Δ$. Recall that a matrix is called $Δ$-modular if the maximum of the absolute values of its $m \times m$ minors equals $Δ$.

math.CO↗
arXiv2026

The Shadow Price of Intelligence: Quality Degradation in LLM Inference as a Supply Chain Problem

Large language model providers are compute constrained, and a common response to congestion is to degrade service. A degraded answer fails with some probability, and a failed answer either returns as a retry or departs as churn, destroying LTV on an unaccounted ledger. We model inference allocation as a newsvendor whose stockout cost is churned lifetime value, a geometric retry multiplier in which the recycled product is dissatisfaction, and a two-regime transient fluid queue whose arrival rate is made endogenous by retries. Statically, there is a regime in which a cheaper model saves energy per initiated task while consuming strictly more capacity per initiated task, so the discount inverts when capacity binds. Dynamically, a reactive throttle fired during a surge can cross an ignition threshold beyond which it manufactures more traffic than it sheds, and a release rule set below the degraded equilibrium converts a transient surge into a permanent degraded regime. With heterogeneous customers, throttling is a transportation problem in retry-inflated load whose optimal policy rations intelligence by critical ratio, and whose dual, the shadow price of intelligence, prices a marginal query by class and by hour. Under congestion, throttling is not a cost lever but a demand lever.

math.OC↗
arXiv2026

Sequential Euclidean connections with exponential memory: distributional performance and adversarial robustness

Points in the unit ball of $\mathbb R^d$ are processed sequentially. Each new point $p_i$ is connected to a state $x_{i-1}$ that summarizes earlier observations, after which $x_i=γx_{i-1}+(1-γ)p_i$, with $0\leqγ\leq1$. The cost is the sum of the $α$-powers of the connection lengths. This constant-gain rule interpolates between the input-order path and the star centered at the initial point. For independent uniform points, we establish the stationary insertion-length distribution and prove that it decreases in stochastic order as $γ$ increases. If $d+α>2$, or if $(d,α)=(1,1)$, the optimal constant parameter satisfies $1-γ_N^*=Θ(N^{-1/2})$, with an explicit asymptotic constant and closed bounds. For $α=1$, its leading expected tree length equals that of the center star and is eventually smaller than the expected lengths of both endpoint constructions. For $α=2$, the optimizer is unique and characterized exactly. For the same $N$, choosing $1-γ_N$ as a fixed positive multiple of $N^{-1/2}$ gives a sharp two-term expansion of the expected uniform-input cost and a maximal adversarial mean cost of $1+O(N^{-1/2})$. For every fixed $0\leqγ<1$ and $0<α\leq3$, the exact asymptotic adversarial value is $(2/(1+γ))^α$. When $d\geq2$, exponential weighting is within a factor smaller than $1.161^α$ of the best fixed nonnegative weighted rule with the same average look-back, for $0<α\leq3$. Comparison with the running mean highlights its time-homogeneous update, stationary coefficient profile, and fixed effective memory.

cs.CG↗
Compare source metadata on this page
WorkPublishedSource identifierSource
Linear Coding of LTI Sources Over Vector Gaussian Channels: A Majorization Approach2026-08-302608.29511arxiv
Which LLM for Which Work? Budgeted Model Allocation under Uncertain Evaluation2026-08-302608.29560arxiv
Reciprocal-Manifold Annealed KKT Flows for Constrained Optimization: Application to the Nonconvex AC Optimal Power Flow2026-08-302608.29628arxiv
Transformer-Based Flow Shop Scheduling Using MILP-Generated Training Data2026-08-302608.29690arxiv
Successive design of backstepping observers for parabolic PDE-ODE systems and its duality to state feedback stabilization2026-08-302608.29693arxiv
A Unified Perspective on Conformal Prediction and Wasserstein Distributionally Robust Optimization for Uncertainty Quantification2026-08-302608.29789arxiv
Quiver Semistability and Structured Kalman Decompositions for Networked Linear Dynamical Systems2026-08-302608.29871arxiv
Finite Sample Identification of Analytic Nonlinear Systems2026-08-302608.29908arxiv
On the suboptimality of stochastic MPC with varying constraint horizon2026-08-302608.30017arxiv
A note on the $Σ_2^P$-completeness of the Frobenius number2026-08-302608.30036arxiv
Rates of Convergence in the Central Limit Theorem for Markov Chains, with an Application to TD Learning2026-08-292401.15719arxiv
Equilibria in Network Constrained Markets with System Operator2026-08-292501.00191arxiv
Aspiration-based Perturbed Learning Automata in Weakly-Acyclic Games with Noisy Utility Measurements2026-08-292511.18418arxiv
Tensor-Based Reduced-Order Modeling for Optimization-Based Inverse Problems2026-08-292607.12613arxiv
Fast Trainable Multilinear Bases for Image Compression2026-10-112608.00053arxiv
Column Number of Delta-modular matrices: Refined Analysis via Sauer Matrices2026-08-292608.06215arxiv
The Shadow Price of Intelligence: Quality Degradation in LLM Inference as a Supply Chain Problem2026-10-072608.23986arxiv
Sequential Euclidean connections with exponential memory: distributional performance and adversarial robustness2026-08-292608.25298arxiv

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