arXiv subjects

Russell Bent

Publications and source records attributed to Russell Bent.

At least 19 recordsLinked to original sources

arXiv2026

The Price of Feasibility: Greedy Approximation Bounds for String Supermodular Optimization over Oracle-Conditioned Greedoids

Greedy algorithms efficiently approximate combinatorial optimization problems, but their guarantees weaken when feasibility couples combinatorial structure with global physical constraints. We study monotone nondecreasing supermodular minimization over the bases of a graphic greedoid under physics-induced constraints. We model physics-informed selection using a look-ahead oracle that identifies candidates extendable to a feasible basis, yielding the Conditioned Sequential Greedy Algorithm. We derive a closed-form approximation bound, which we call the price of feasibility, based on the variability of oracle-restricted candidate sets and a probabilistic correction for unobserved elements. As a case study, we show that FORWARD, an algorithm for multi-source radial network reconfiguration, instantiates this framework. Numerical results demonstrate the tightness of the bound and quantify the feasibility-optimality trade-off.

math.OC↗

arXiv2026

Smoothed Two-Stage Decomposition Algorithm for Solving Large-Scale Transmission and Distribution AC-OPF Problems

The integration of distributed energy resources (DERs) into the power grid has introduced new challenges to AC optimal power flow (AC-OPF) problems. Traditional OPF optimize consider transmission systems, treating distribution networks as static loads. However, the growing presence of DERs makes accurate distribution system modeling crucial for grid operations. Consequently, efficiently solving the resultant large-scale, nonconvex transmission and distribution (T&D) AC-OPF problem remains a significant challenge. This paper proposes a Smoothed Two-Stage Decomposition Optimizer (StsDOpt) to address these complexities by decomposing the T&D AC-OPF problem into a master-subproblem(s) structure, enabling parallel solving. Unlike traditional methods, StsDOpt does not rely on approximations or relaxations. It uses a smoothing technique to render the subproblems responses differentiable with respect to the master problem, leveraging the barrier problem properties inherent in primal-dual interior point methods. This approach is crucial for accurately modeling and solving distribution systems, which are multiphase, unbalanced, and nonlinear, distinguishing StsDOpt apart from other methods. Integrated into the PowerModelsITD framework, StsDOpt has been validated through numerical experiments, demonstrating reduced wall-clock solve time and increased scalability. Results highlight its efficacy as a robust, scalable solution for large-scale T&D AC-OPF problems, facilitating the reliable integration of DERs into complex T&D systems.

math.OC↗

arXiv2026

PACR: Parameter-Optimized AC Power Flow Restoration for AC Feasible DCOPF Dispatch

The DC optimal power flow is widely used in power system operations because of its computational efficiency and scalability. However, DC dispatches are not guaranteed to satisfy the nonlinear AC power-flow equations or associated operational limits. This paper develops a parameterized, differentiable AC power-flow restoration method for mapping DC dispatches to AC-consistent operating points. The method incorporates distributed slack for active-power balancing and PV/PQ switching for reactive-power regulation, both implemented using smooth differentiable surrogates with tunable parameters, including slack participation factors, voltage setpoints, and regulation steepness. These parameters are trained offline by differentiating through the AC restoration equations using the implicit function theorem. Once trained, the optimized parameters are fixed and used directly during AC power-flow recovery from DC dispatches. The approach is evaluated on IEEE, ACTIVSg, and PEGASE test systems using setpoints computed by standard DC optimal power flow. Results show that the optimized restoration method improves AC feasibility recovery across various systems relative to conventional single-slack AC power-flow recovery. On the 9,241-bus case, the optimized method improves cost difference by 80% relative to the conventional recovery baseline and improves solving time relative to ACOPF by 75%.

eess.SY↗

arXiv2026

An Agentic Orchestration of Atomistic Simulations

Atomistic simulations are central to materials design, but their execution involves complex, multi-step workflows that require significant human expertise. Here, we present an agent-based system embedded within the URSA (Universal Research and Scientific Agent) framework that automates the design, execution, and validation of atomistic simulations, demonstrated using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) tool. Our system autonomously selects interatomic potentials, constructs and runs simulations, and performs iterative error recovery within a closed-loop workflow. We evaluate the scientific reliability of the agent by benchmarking its outputs against LAVA, a high-throughput toolkit for LAMMPS and the Vienna Ab initio Simulation Package (VASP) calculations. Our framework reduces manual intervention and trial-and-error, thereby improving the rigor, reproducibility, and scalability of atomistic modeling.

cs.AI↗

arXiv2026

Hierarchical Prompt-Domain Control and Learning for Resource-Constrained Agentic Language Models

Large Language Models are increasingly deployed inside agentic systems, where they must follow structured protocols, adapt to evolving states, and operate under memory, latency, and cost constraints. In such regimes, prompt extension is unreliable: growing contexts can push compact models outside their effective prompt domain, while deployment-time fine-tuning remains limited by scarce data and compute. We propose a hierarchical control-and-learning framework in which a compact model is first distilled to learn the required output schema, then supervised online by an oracle-controller loop. The controller monitors protocol validity and semantic performance, projects accumulated histories into a feasible prompt domain, and triggers lightweight oracle-supervised fine-tuning under drift. This separates schema learning for communication compatibility from semantic adaptation for task-level correction. We formalize prompt-domain feasibility and attention-induced saturation, motivating control of the effective prompt state rather than reliance on nominal context length. Using Multi-Fidelity Bayesian Optimization as a controlled sequential testbed, we characterize a core deployment failure mode and show improved reliability and cost-efficiency over non-hierarchical, distillation-only, and non-distilled baselines.

cs.AI↗

arXiv2026

Chain-based Adaptive Reconfiguration Over Lattices for Hallucination Reduction

We introduce CAROL (Chain-based Adaptive Reconfiguration Over Lattices), a probabilistic framework for test-time hallucination reduction in large language models. Rather than relying on token-level uncertainty, CAROL defines a semantic uncertainty measure based on the consistency between generated responses and a trusted context, inducing a string-submodular objective over a lattice of textual sequences. This formulation enables hallucination mitigation to be cast as a Markov chain accept-reject process with provable convergence and near-optimality guarantees, allowing the model to iteratively refine outputs toward semantic consistency. By operating at the level of meaning, CAROL unifies hallucination detection and mitigation within a single framework. Empirical results on question answering and multi-agent reasoning benchmarks show that CAROL significantly reduces hallucinations and improves reliability and interpretability compared to likelihood-based and retrieval-augmented baselines, while maintaining competitive computational efficiency.

cs.CL↗

arXiv2026

Efficient Graph Partitioning under Resource Constraints: A Cutting-Plane Framework for Distribution Grids

This paper presents an optimal network topology control framework using cutting-plane methods for efficient network partitioning with controllable edges. The objective is to enable real-time reconfiguration of interconnected sub-networks while ensuring radial connectivity, resource feasibility, and structured leader allocation, which are essential for distributed control, stability, and coordination. The problem is formulated as a mixed-integer program that integrates graph-theoretic constraints, resource flow, and network structural properties to enforce an operational hierarchy. To address the combinatorial complexity of cycle elimination and leader assignment, we propose an iterative cutting-plane framework that ensures convergence to an optimal and feasible network topology. Theoretical guarantees on optimality preservation, feasibility, and convergence are established, ensuring systematic elimination of infeasible configurations while maintaining distributed controllability. Simulations on a modified Iowa 240-bus power distribution grid demonstrate the framework's effectiveness in network reconfiguration under resource constraints. The approach achieves median and best-case speedups of 57.5x and over 64x in a 46-switch configuration, highlighting its applicability to other networked control systems.

math.OC↗

arXiv2026

Load Block Modeling in Distribution Systems: Network Reconfiguration for Load Restoration

The distribution system restoration (DSR) problem has received considerable attention over the last decade or more. Solutions to the DSR problem identify the best set or sequence of actions to perform on a distribution circuit to restore service after a disruption. The problem is challenging from a computational perspective, with engineering constraints specific to distribution systems, such as radial operations, that are difficult to effectively model. In this paper, we revisit the model for how specific loads are shed, energized and restored--and develop a formulation that more accurately models the requirements of load shedding, load energizing and restoration in distribution systems.

eess.SY↗

arXiv2026

A Hybrid Decomposition Approach for Stochastic Unit Commitment with Combined-Cycle Generators

The U.S. power grid is undergoing a paradigm shift as energy demand grows in scale and volatility. In response to this growing need, the U.S. has increased adoption of combined-cycle generators (CCs). CCs are fast-ramping generators that utilize variable configurations of combustion turbines (CTs) and steam turbines (STs) to achieve higher efficiency than traditional CTs. For schedule optimization, modeling these CCs requires the addition of a large number of binary constraints and variables to Unit Commitment (UC) problem formulations. This paper presents a novel hybrid Benders' (BD) and Dantzig-Wolfe (DW) decomposition algorithm, called CRG, for stochastic UC problems with CCs. CRG exploits the separability of the linear constraints in UC through BD and the integer CC constraints through DW. A novel set of valid inequalities are proposed for significantly tightening the lower bound produced by CRG. CRG is tested on the 935-generator FERC test data set, modified to include CC mode data. Results demonstrate better primal solutions than BD on cases with at least 20 load scenarios. CRG scales computationally better than Gurobi's branch-and-bound solver, which exceeds 64GB RAM allocations at 45 scenarios. Results show that the proposed algorithm is a scalable approach for solving large-scale stochastic UC with CCs.

math.OC↗

arXiv2026

Exploiting block triangular submatrices in KKT systems

We propose a method for solving Karush-Kuhn-Tucker (KKT) systems that exploits block triangular submatrices by first using a Schur complement decomposition to isolate the block triangular submatrices then performing a block backsolve where only diagonal blocks of the block triangular form need to be factorized. We show that factorizing reducible symmetric-indefinite matrices with standard 1$\times$1 or 2$\times$2 pivots yields fill-in outside the diagonal blocks of the block triangular form, in contrast to our proposed method. While exploiting a block triangular submatrix has limited fill-in, unsymmetric matrix factorization methods do not reveal inertia, which is required by interior point methods for nonconvex optimization. We show that our target matrix has inertia that is known \textit{a priori}, letting us compute inertia of the KKT matrix by Sylvester's law. Finally, we demonstrate the computational advantage of this method on KKT systems from optimization problems with neural network surrogates in their constraints. Our method achieves up to 15$\times$ speedups over state-of-the-art symmetric indefinite matrix factorization methods MA57 and MA86 in a constant-hardware comparison.

math.OC↗

arXiv2026

E-Globe: Scalable $\epsilon$-Global Verification of Neural Networks via Tight Upper Bounds and Pattern-Aware Branching

Neural networks achieve strong empirical performance, but robustness concerns still hinder deployment in safety-critical applications. Formal verification provides robustness guarantees, but current methods face a scalability-completeness trade-off. We propose a hybrid verifier in a branch-and-bound (BaB) framework that efficiently tightens both upper and lower bounds until an $\epsilon-$global optimum is reached or early stop is triggered. The key is an exact nonlinear program with complementarity constraints (NLP-CC) for upper bounding that preserves the ReLU input-output graph, so any feasible solution yields a valid counterexample and enables rapid pruning of unsafe subproblems. We further accelerate verification with (i) warm-started NLP solves requiring minimal constraint-matrix updates and (ii) pattern-aligned strong branching that prioritizes splits most effective at tightening relaxations. We also provide conditions under which NLP-CC upper bounds are tight. Experiments on MNIST and CIFAR-10 show markedly tighter upper bounds than PGD across perturbation radii spanning up to three orders of magnitude, fast per-node solves in practice, and substantial end-to-end speedups over MIP-based verification, amplified by warm-starting, GPU batching, and pattern-aligned branching.

cs.LG↗

arXiv2026

Water Demand Maximization: Quick Recovery of Nonlinear Physics Solutions

Determining the maximum demand a water distribution network can satisfy is crucial for ensuring reliable supply and planning network expansion. This problem, typically formulated as a mixed-integer nonlinear program (MINLP), is computationally challenging. A common strategy to address this challenge is to solve mixed-integer linear program (MILP) relaxations derived by partitioning variable domains and constructing linear over- and under-estimators to nonlinear constraints over each partition. While MILP relaxations are easier to solve up to a modest level of partitioning, their solutions often violate nonlinear water flow physics. Thus, recovering feasible MINLP solutions from the MILP relaxations is crucial for enhancing MILP-based approaches. In this paper, we propose a robust solution recovery method that efficiently computes feasible MINLP solutions from MILP relaxations, regardless of partition granularity. Combined with iterative partition refinement, our method generates a sequence of feasible solutions that progressively approach the optimum. Through extensive numerical experiments, we demonstrate that our method outperforms baseline methods and direct MINLP solves by consistently recovering high-quality feasible solutions with significantly reduced computation times.

math.OC↗

arXiv2025

Towards AC Feasibility of DCOPF Dispatch

DC Optimal Power Flow (DCOPF) is widely utilized in power system operations due to its simplicity and computational efficiency. However, its lossless, reactive power-agnostic model often yields dispatches that are infeasible under practical operating scenarios such as the nonlinear AC power flow (ACPF) equations. While theoretical analysis demonstrates that DCOPF solutions are inherently AC-infeasible, their widespread industry adoption suggests substantial practical utility. This paper develops a unified DCOPF-ACPF pipeline to recover AC feasible solutions from DCOPF-based dispatches. The pipeline uses four DCOPF variants and applies AC feasibility recovery using both distributed slack allocation and PV/PQ switching. The main objective is to identify the most effective pipeline for restoring AC feasibility. Evaluation across over 10,000 dispatch scenarios on various test cases demonstrates that the structured ACPF model yields solutions that satisfy both the ACPF equations, and all engineering inequality constraints. In a 13,659 bus case, the mean absolute error and cost differences between DCOPF and ACOPF are reduced by 75% and 93%, respectively, compared to conventional single slack bus methods. Under extreme loading conditions, the pipeline reduces inequality constraint violations by a factor of 3 to 5.

eess.SY↗

arXiv2025

Constraint-Informed Active Learning for End-to-End ACOPF Optimization Proxies

This paper studies optimization proxies, machine learning (ML) models trained to efficiently predict optimal solutions for AC Optimal Power Flow (ACOPF) problems. While promising, optimization proxy performance heavily depends on training data quality. To address this limitation, this paper introduces a novel active sampling framework for ACOPF optimization proxies designed to generate realistic and diverse training data. The framework actively explores varied, flexible problem specifications reflecting plausible operational realities. More importantly, the approach uses optimization-specific quantities (active constraint sets) that better capture the salient features of an ACOPF that lead to the optimal solution. Numerical results show superior generalization over existing sampling methods with an equivalent training budget, significantly advancing the state-of-practice for trustworthy ACOPF optimization proxies.

cs.LG↗

arXiv2025

Microgrids optimal radial reconfiguration via FORWARD algorithm

Microgrids offer a promising paradigm for integrating distributed energy resources, bolstering energy resilience, and reducing the impact of blackouts. However, their inherent decentralization and dynamic operation present substantial energy management complexities. These complexities, including balancing supply and demand, ensuring system stability, and minimizing operational costs, often necessitate solving computationally intractable NP-hard Mixed-Integer Non-Linear Programming (MINLP) problems. Traditional MINLP solvers struggle with the scalability and feasibility guarantees required for these challenges. To address this, this paper tackles the problem of resource allocation and radial configuration design for microgrid power distribution and proposes and abstracted problem which is solved by introducing a permutation-based iterative search method over the recently introduced FORWARD method to efficiently identify feasible, near-optimal radial network structures while inherently respecting physical constraints. Furthermore, this paper investigates the integration of the proposed method as a warm-start strategy for benchmark MINLP solvers offering a scalable solution for comprehensive microgrid design.

eess.SY↗

arXiv2025

A General and Streamlined Differentiable Optimization Framework

Differentiating through constrained optimization problems is increasingly central to learning, control, and large-scale decision-making systems, yet practical integration remains challenging due to solver specialization and interface mismatches. This paper presents a general and streamlined framework-an updated DiffOpt.jl-that unifies modeling and differentiation within the Julia optimization stack. The framework computes forward - and reverse-mode solution and objective sensitivities for smooth, potentially nonconvex programs by differentiating the KKT system under standard regularity assumptions. A first-class, JuMP-native parameter-centric API allows users to declare named parameters and obtain derivatives directly with respect to them - even when a parameter appears in multiple constraints and objectives - eliminating brittle bookkeeping from coefficient-level interfaces. We illustrate these capabilities on convex and nonconvex models, including economic dispatch, mean-variance portfolio selection with conic risk constraints, and nonlinear robot inverse kinematics. Two companion studies further demonstrate impact at scale: gradient-based iterative methods for strategic bidding in energy markets and Sobolev-style training of end-to-end optimization proxies using solver-accurate sensitivities. Together, these results demonstrate that differentiable optimization can be deployed as a routine tool for experimentation, learning, calibration, and design-without deviating from standard JuMP modeling practices and while retaining access to a broad ecosystem of solvers.

cs.LG↗

arXiv2025

FORWARD: A Feasible Radial Reconfiguration Algorithm for Multi-Source Distribution Networks

This paper considers an optimal radial reconfiguration problem in multi-source distribution networks, where the goal is to find a radial configuration that minimizes quadratic distribution costs while ensuring all sink demands are met. This problem arises in critical infrastructure systems such as power distribution, water networks, and gas distribution, where radial configurations are essential for operational safety and efficiency. Optimal solution for this problem is known to be NP-hard. In this paper, we prove further that constructing a feasible radial distribution configuration is weakly NP-complete, making exact solution methods computationally intractable for large-scale networks. We propose FORWARD (Feasibility Oriented Random-Walk Inspired Algorithm for Radial Reconfiguration in Distribution Networks), a polynomial-time algorithm that leverages graph-theoretic decomposition and random walk principles to construct feasible radial configurations. Our approach introduces novel techniques including strategic graph partitioning at articulation points, dual graph condensation to address greedy shortsightedness, and capacity-aware edge swapping for infeasibility resolution. We provide rigorous theoretical analysis proving feasibility guarantees and establish a compositional framework enabling parallel processing while preserving optimality properties. Comprehensive numerical evaluation on networks ranging from IEEE standard test systems to 400-node small-world networks demonstrates that FORWARD consistently outperforms commercial MINLP solvers, achieving optimal or near-optimal solutions in seconds where traditional methods require hours or fail entirely. The algorithm's polynomial-time complexity and scalability make it particularly suitable for real-time distribution network management and as an effective initialization strategy for iterative optimization solvers.

math.OC↗

arXiv2025

Nonlinear Optimization with GPU-Accelerated Neural Network Constraints

We propose a reduced-space formulation for optimizing over trained neural networks where the network's outputs and derivatives are evaluated on a GPU. To do this, we treat the neural network as a "gray box" where intermediate variables and constraints are not exposed to the optimization solver. Compared to the full-space formulation, in which intermediate variables and constraints are exposed to the optimization solver, the reduced-space formulation leads to faster solves and fewer iterations in an interior point method. We demonstrate the benefits of this method on two optimization problems: Adversarial generation for a classifier trained on MNIST images and security-constrained optimal power flow with transient feasibility enforced using a neural network surrogate.

cs.LG↗