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Optimization is a ubiquitous modeling tool and is often deployed in settings which repeatedly solve similar instances of the same problem. Amortized optimization methods use learning to predict the solutions to problems in these settings,…

Machine Learning · Computer Science 2025-10-07 Brandon Amos

Optimal transport problems pose many challenges when considering their numerical treatment. We investigate the solution of a PDE-constrained optimisation problem subject to a particular transport equation arising from the modelling of image…

Numerical Analysis · Mathematics 2018-01-15 Roland Herzog , John W. Pearson , Martin Stoll

Incorporating a non-Euclidean variable metric to first-order algorithms is known to bring enhancement. However, due to the lack of an optimal choice, such an enhancement appears significantly underestimated. In this work, we establish a…

Optimization and Control · Mathematics 2023-11-21 Yifan Ran

The paper proposes and justifies a new algorithm of the proximal Newton type to solve a broad class of nonsmooth composite convex optimization problems without strong convexity assumptions. Based on advanced notions and techniques of…

Optimization and Control · Mathematics 2022-03-02 Boris S. Mordukhovich , Xiaoming Yuan , Shangzhi Zeng , Jin Zhang

This paper examines a variety of classical optimization problems, including well-known minimization tasks and more general variational inequalities. We consider a stochastic formulation of these problems, and unlike most previous work, we…

Optimization and Control · Mathematics 2025-11-11 Vladimir Solodkin , Andrew Veprikov , Aleksandr Beznosikov

Non-discrimination is a recognized objective in algorithmic decision making. In this paper, we introduce a novel probabilistic formulation of data pre-processing for reducing discrimination. We propose a convex optimization for learning a…

Machine Learning · Statistics 2017-04-12 Flavio P. Calmon , Dennis Wei , Karthikeyan Natesan Ramamurthy , Kush R. Varshney

In this short note, we discuss a goal-oriented multiobjective optimization problem for system performance assessment. The objective function for such optimization problem, which is usually a composite of different performance indices…

Optimization and Control · Mathematics 2020-06-12 Getachew K Befekadu

We address composite optimization problems, which consist in minimizing the sum of a smooth and a merely lower semicontinuous function, without any convexity assumptions. Numerical solutions of these problems can be obtained by proximal…

Optimization and Control · Mathematics 2024-02-14 Alberto De Marchi

For minimizing a strongly convex objective function subject to linear inequality constraints, we consider a penalty approach that allows one to utilize stochastic methods for problems with a large number of constraints and/or objective…

Optimization and Control · Mathematics 2022-02-16 Meng Li , Paul Grigas , Alper Atamturk

The predict+optimize problem combines machine learning ofproblem coefficients with a combinatorial optimization prob-lem that uses the predicted coefficients. While this problemcan be solved in two separate stages, it is better to…

Machine Learning · Computer Science 2020-12-07 Ali Ugur Guler , Emir Demirovic , Jeffrey Chan , James Bailey , Christopher Leckie , Peter J. Stuckey

This paper presents a comprehensive survey of methods which can be utilized to search for solutions to systems of nonlinear equations (SNEs). Our objectives with this survey are to synthesize pertinent literature in this field by presenting…

Mathematical Software · Computer Science 2022-08-19 Ilias S. Kotsireas , Panos M. Pardalos , Alexander Semenov , William T. Trevena , Michael N. Vrahatis

In this paper, we propose a multilevel stochastic framework for the solution of nonconvex unconstrained optimization problems. The proposed approach uses random regularized first-order models that exploit an available hierarchical…

Optimization and Control · Mathematics 2025-11-27 Filippo Marini , Margherita Porcelli , Elisa Riccietti

Nonlinear optimization-based control policies, such as those those arising in nonlinear Model Predictive Control, have seen remarkable success in recent years. These policies require solving computationally demanding nonlinear optimization…

Optimization and Control · Mathematics 2025-12-02 Riccardo Zuliani , Efe C. Balta , John Lygeros

A general, variational approach to derive low-order reduced systems for nonlinear systems subject to an autonomous forcing, is introduced. The approach is based on the concept of optimal parameterizing manifold (PM) that substitutes the…

Dynamical Systems · Mathematics 2020-01-08 Mickaël D. Chekroun , Honghu Liu , James C. McWilliams

Newton's method is a fundamental technique in optimization with quadratic convergence within a neighborhood around the optimum. However reaching this neighborhood is often slow and dominates the computational costs. We exploit two…

Machine Learning · Computer Science 2016-05-24 Hadi Daneshmand , Aurelien Lucchi , Thomas Hofmann

Optimization networks are a new methodology for holistically solving interrelated problems that have been developed with combinatorial optimization problems in mind. In this contribution we revisit the core principles of optimization…

In this paper, we study a first order solution method for a particular class of set optimization problems where the solution concept is given by the set approach. We consider the case in which the set-valued objective mapping is identified…

Optimization and Control · Mathematics 2021-07-27 Gemayqzel Bouza , Ernest Quintana , Christiane Tammer

Sequential implicit (SI) formulations are gaining increasing interest due to their ability to decouple reservoir simulation problems into distinct flow and transport subproblems, allowing for the use of specialized solvers tailored to each.…

Numerical Analysis · Mathematics 2025-04-29 Omar Chaabi , Mohammed Al-Kobaisi

We consider several classes of highly important semidefinite optimization problems that involve both a convex objective function (smooth or nonsmooth) and additional linear or nonlinear smooth and convex constraints, which are ubiquitous in…

Optimization and Control · Mathematics 2025-04-08 Dan Garber , Atara Kaplan

We propose a general-purpose method for finding high-quality solutions to hard optimization problems, inspired by self-organizing processes often found in nature. The method, called Extremal Optimization, successively eliminates extremely…

Statistical Mechanics · Physics 2018-07-06 S. Boettcher , A. Percus