English
Related papers

Related papers: Cardinality-Constrained Multi-Objective Optimizati…

200 papers

Multi-objective optimization aims at finding trade-off solutions to conflicting objectives. These constitute the Pareto optimal set. In the context of expensive-to-evaluate functions, it is impossible and often non-informative to look for…

Machine Learning · Statistics 2020-02-20 David Gaudrie , Rodolphe Le Riche , Victor Picheny , Benoit Enaux , Vincent Herbert

In this work, we propose a novel method to tackle the problem of multiobjective optimization under parameteric uncertainties, by considering the Conditional Pareto Sets and Conditional Pareto Fronts. Based on those quantities we can define…

Optimization and Control · Mathematics 2026-01-15 Victor Trappler , Céline Helbert , Rodolphe Le Riche

In this paper, we consider the cardinality-constrained optimization problems and propose a new sequential optimality condition for the continuous relaxation reformulation which is popular recently. It is stronger than the existing results…

Optimization and Control · Mathematics 2021-10-05 Liping Pang , Menglong Xue , Na Xu

Necessary conditions for high-order optimality in smooth nonlinear constrained optimization are explored and their inherent intricacy discussed. A two-phase minimization algorithm is proposed which can achieve approximate first-, second-…

Optimization and Control · Mathematics 2021-05-31 C. Cartis , N. I. M. Gould , Ph. L. Toint

In sparse optimization, enforcing hard constraints using the $\ell_0$ pseudo-norm offers advantages like controlled sparsity compared to convex relaxations. However, many real-world applications demand not only sparsity constraints but also…

Optimization and Control · Mathematics 2025-06-12 William de Vazelhes , Xiao-Tong Yuan , Bin Gu

The first-order optimality conditions of sparse bilinear least squares problems are studied. The so-called T-type and N-type stationary points for this problem are characterized in terms of tangent cone and normal cone in Bouligand and…

Optimization and Control · Mathematics 2026-01-21 Zixin Deng , Zheng-Hai Huang , Yun-Bin Zhao

This paper is devoted to studying the stationary solutions of a general constrained optimization problem through its associated unconstrained penalized problems. We aim to answer the question, "what do the stationary solutions of a…

Optimization and Control · Mathematics 2022-06-28 Ashkan Mohammadi

We present a novel algorithm that allows us to gain detailed insight into the effects of sparsity in linear and nonlinear optimization, which is of great importance in many scientific areas such as image and signal processing, medical…

Optimization and Control · Mathematics 2021-09-23 Katharina Bieker , Bennet Gebken , Sebastian Peitz

In this paper, we present some new necessary and sufficient optimality conditions in terms of the Clarke subdifferentials for approximate Pareto solutions of a nonsmooth vector optimization problem which has an infinite number of…

Optimization and Control · Mathematics 2019-05-14 Ta Quang Son , Nguyen Van Tuyen , Ching-Feng Wen

This paper deals with Pareto solutions of a nonsmooth fractional interval-valued multiobjective optimization. We first introduce four types of Pareto solutions of the considered problem by considering the lower-upper interval order relation…

Optimization and Control · Mathematics 2022-12-26 Nguyen Huy Hung , Nguyen Van Tuyen

Tasks in multi-task learning often correlate, conflict, or even compete with each other. As a result, a single solution that is optimal for all tasks rarely exists. Recent papers introduced the concept of Pareto optimality to this field and…

Machine Learning · Computer Science 2020-08-28 Pingchuan Ma , Tao Du , Wojciech Matusik

Regularized optimal transport (OT) is now increasingly used as a loss or as a matching layer in neural networks. Entropy-regularized OT can be computed using the Sinkhorn algorithm but it leads to fully-dense transportation plans, meaning…

Machine Learning · Statistics 2023-04-17 Tianlin Liu , Joan Puigcerver , Mathieu Blondel

Constrained single-objective problems have been frequently tackled by evolutionary multi-objective algorithms where the constraint is relaxed into an additional objective. Recently, it has been shown that Pareto optimization approaches…

Neural and Evolutionary Computing · Computer Science 2024-06-10 Frank Neumann , Carsten Witt

Deep learning models form one of the most powerful machine learning models for the extraction of important features. Most of the designs of deep neural models, i.e., the initialization of parameters, are still manually tuned. Hence,…

Machine Learning · Computer Science 2023-05-18 Mrittika Chakraborty , Wreetbhas Pal , Sanghamitra Bandyopadhyay , Ujjwal Maulik

We survey optimization problems that involve the cardinality of variable vectors in constraints or the objective function. We provide a unified viewpoint on the general problem classes and models, and give concrete examples from diverse…

Optimization and Control · Mathematics 2022-08-09 Andreas M. Tillmann , Daniel Bienstock , Andrea Lodi , Alexandra Schwartz

Efficiently solving multi-objective optimization problems for simulation optimization of important scientific and engineering applications such as materials design is becoming an increasingly important research topic. This is due largely to…

Artificial Intelligence · Computer Science 2023-06-27 Eric Hans Lee , Bolong Cheng , Michael McCourt

Scalarization allows to solve a multi-objective optimization problem by solving many single-objective sub-problems, uniquely determined by some parameters. In this work, we propose several adaptive strategies to select such parameters in…

Optimization and Control · Mathematics 2022-11-08 Giacomo Borghi

We consider the maximum likelihood estimation of sparse inverse covariance matrices. We demonstrate that current heuristic approaches primarily encourage robustness, instead of the desired sparsity. We give a novel approach that solves the…

Machine Learning · Statistics 2021-11-08 Dimitris Bertsimas , Jourdain Lamperski , Jean Pauphilet

In this article we develop a gradient-based algorithm for the solution of multiobjective optimization problems with uncertainties. To this end, an additional condition is derived for the descent direction in order to account for…

Optimization and Control · Mathematics 2018-08-02 Sebastian Peitz , Michael Dellnitz

Pareto optimization via evolutionary multi-objective algorithms has been shown to efficiently solve constrained monotone submodular functions. Traditionally when solving multiple problems, the algorithm is run for each problem separately.…

Neural and Evolutionary Computing · Computer Science 2026-04-17 Liam Wigney , Frank Neumann