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Related papers: Proving Global Optimality of ACOPF Solutions

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We investigate the proximal point algorithm (PPA) and its inexact extensions under an error bound condition, which guarantees a global linear convergence if the proximal regularization parameter is larger than the error bound condition…

Optimization and Control · Mathematics 2021-02-26 Meng Lu , Zheng Qu

We compare full-space, reduced-space, and gray-box formulations for representing trained neural networks in nonlinear constrained optimization problems. We test these formulations on a transient stability-constrained, security-constrained…

Machine Learning · Computer Science 2024-12-17 Robert B. Parker , Oscar Dowson , Nicole LoGiudice , Manuel Garcia , Russell Bent

The paper presents a priori error analysis of the shallow neural network approximation to the solution to the indefinite elliptic equation and and cutting-edge implementation of the Orthogonal Greedy Algorithm (OGA) tailored to overcome the…

Numerical Analysis · Mathematics 2024-10-28 Qingguo Hong , Jiwei Jia , Young Ju Lee , Ziqian Li

The alternating-current optimal power flow (ACOPF) is one of the best known non-convex non-linear optimisation problems. We present a novel re-formulation of ACOPF, which is based on lifting the rectangular power-voltage rank-constrained…

Optimization and Control · Mathematics 2018-02-20 Jakub Marecek , Martin Takac

In practice, optimization tasks have some structure that allows developing new algorithms for every problem with faster convergence rates. Using the structure of optimization tasks, we can propose algorithms with more optimistic convergence…

Optimization and Control · Mathematics 2020-09-01 Alexander Tyurin

Branch-and-bound-based consensus maximization stands out due to its important ability of retrieving the globally optimal solution to outlier-affected geometric problems. However, while the discovery of such solutions caries high scientific…

Computer Vision and Pattern Recognition · Computer Science 2024-03-21 Xinyue Zhang , Liangzu Peng , Wanting Xu , Laurent Kneip

Large-scale non-convex sparsity-constrained problems have recently gained extensive attention. Most existing deterministic optimization methods (e.g., GraSP) are not suitable for large-scale and high-dimensional problems, and thus…

Machine Learning · Computer Science 2019-12-03 Fanhua Shang , Bingkun Wei , Hongying Liu , Yuanyuan Liu , Jiacheng Zhuo

This paper proposes a two-level distributed algorithmic framework for solving the AC optimal power flow (OPF) problem with convergence guarantees. The presence of highly nonconvex constraints in OPF poses significant challenges to…

Optimization and Control · Mathematics 2021-06-14 Kaizhao Sun , Xu Andy Sun

In computer science, there exist a large number of optimization problems defined on graphs, that is to find a best node state configuration or a network structure such that the designed objective function is optimized under some…

Machine Learning · Computer Science 2020-04-17 Yaoxin Li , Jing Liu , Guozheng Lin , Yueyuan Hou , Muyun Mou , Jiang Zhang

In this study, we propose a novel gap-constraint-based reformulation for optimal control problems with equilibrium constraints (OCPECs). We show that the proposed reformulation generates a new constraint system equivalent to the original…

Optimization and Control · Mathematics 2024-06-06 Kangyu Lin , Toshiyuki Ohtsuka

We introduce LiPopt, a polynomial optimization framework for computing increasingly tighter upper bounds on the Lipschitz constant of neural networks. The underlying optimization problems boil down to either linear (LP) or semidefinite…

Machine Learning · Computer Science 2020-04-21 Fabian Latorre , Paul Rolland , Volkan Cevher

This paper addresses the problem of optimizing partition functions in a stochastic learning setting. We propose a stochastic variant of the bound majorization algorithm that relies on upper-bounding the partition function with a quadratic…

Machine Learning · Computer Science 2020-11-04 Jing Wang , Anna Choromanska

We explore why many recently proposed robust estimation problems are efficiently solvable, even though the underlying optimization problems are non-convex. We study the loss landscape of these robust estimation problems, and identify the…

Machine Learning · Statistics 2020-05-29 Banghua Zhu , Jiantao Jiao , Jacob Steinhardt

This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…

Optimization and Control · Mathematics 2026-02-17 Patrick L. Combettes , Javier I. Madariaga

Determining a globally optimal solution of belief space planning (BSP) in high-dimensional state spaces is computationally expensive, as it involves belief propagation and objective function evaluation for each candidate action. Our…

Robotics · Computer Science 2019-03-05 Andrej Kitanov , Vadim Indelman

We initiate a formal study of reproducibility in optimization. We define a quantitative measure of reproducibility of optimization procedures in the face of noisy or error-prone operations such as inexact or stochastic gradient computations…

Optimization and Control · Mathematics 2022-12-06 Kwangjun Ahn , Prateek Jain , Ziwei Ji , Satyen Kale , Praneeth Netrapalli , Gil I. Shamir

We describe a factor-revealing convex optimization problem for the integrality gap of the maximum-cut semidefinite programming relaxation: for each $n \geq 2$ we present a convex optimization problem whose optimal value is the largest…

Optimization and Control · Mathematics 2021-03-24 Fernando Mário de Oliveira Filho , Frank Vallentin

Federated learning enables training on a massive number of edge devices. To improve flexibility and scalability, we propose a new asynchronous federated optimization algorithm. We prove that the proposed approach has near-linear convergence…

Distributed, Parallel, and Cluster Computing · Computer Science 2020-12-08 Cong Xie , Sanmi Koyejo , Indranil Gupta

Several methods have been proposed in the literature to improve the quality of AC optimal power flow (AC-OPF) datasets used in machine learning (ML) models. Yet, scalability to large power systems remains unaddressed and comparing…

Systems and Control · Electrical Eng. & Systems 2025-08-27 Matteo Baù , Luca Perbellini , Samuele Grillo

We consider the dynamic resource allocation problem where the decision space is finite-dimensional, yet the solution must satisfy a large or even infinite number of constraints revealed via streaming data or oracle feedback. We model this…

Machine Learning · Computer Science 2026-03-18 Yiming Zong , Jiashuo Jiang