Related papers: Optimization over the weakly Pareto set and multi-…
We study the following optimization problem over a dynamical system that consists of several linear subsystems: Given a finite set of $n\times n$ matrices and an $n$-dimensional vector, find a sequence of $K$ matrices, each chosen from the…
This paper studies the sparse Moment-SOS hierarchy of relaxations for solving sparse polynomial optimization problems. We show that this sparse hierarchy is tight if and only if the objective can be written as a sum of sparse nonnegative…
In this paper, we are interested in the existence of Pareto solutions to vector polynomial optimization problems over a basic closed semi-algebraic set. By invoking some powerful tools from real semi-algebraic geometry, we first introduce…
New versions and extensions of Benson's outer approximation algorithm for solving linear vector optimization problems are presented. Primal and dual variants are provided in which only one scalar linear program has to be solved in each…
We provide a sparse version of the bounded degree SOS hierarchy BSOS [7] for polynomial optimization problems. It permits to treat large scale problems which satisfy a structured sparsity pattern. When the sparsity pattern satisfies the…
Benchmark problems play a central role in assessing the performance of numerical optimization algorithms. However, many existing constrained multiobjective optimization benchmark problems rely on overly restricted constructions or lack…
Evolutionary multi-objective algorithms have successfully been used in the context of Pareto optimization where a given constraint is relaxed into an additional objective. In this paper, we explore the use of 3-objective formulations for…
Sparse inverse covariance selection is a fundamental problem for analyzing dependencies in high dimensional data. However, such a problem is difficult to solve since it is NP-hard. Existing solutions are primarily based on convex…
We determine the power of the weighted sum scalarization with respect to the computation of approximations for general multiobjective minimization and maximization problems. Additionally, we introduce a new multi-factor notion of…
We provide a solution method for the polyhedral convex set optimization problem, that is, the problem to minimize a set-valued mapping with polyhedral convex graph with respect to a set ordering relation which is generated by a polyhedral…
This document introduces a strategy to solve linear optimization problems. The strategy is based on the bounding condition each constraint produces on each one of the problem's dimension. The solution of a linear optimization problem is…
A function of a matrix is polyconvex when it can be expressed as a convex function of the matrix minors. Polyconvexity is a regularity condition ensuring existence of minimizers in nonlinear elasticity and, more broadly, in vectorial…
We consider the Moment-SOS hierarchy in polynomial optimization. We first provide a sufficient condition to solve the truncated K-moment problem associated with a given degree-$2n$ pseudo-moment sequence $\phi$ n and a semi-algebraic set $K…
In solving a multi-objective optimization problem by scalarization techniques, solutions to a scalarized problem are, in general, weakly efficient rather than efficient to the original problem. Thus, it is crucial to understand what problem…
We address the problem of testing weak optimality of a given solution of a given interval linear program. The problem was recently wrongly stated to be polynomially solvable. We disprove it. We show that the problem is NP-hard in general.…
This paper aims to find efficient solutions to a multi-objective optimization problem (MP) with convex polynomial data. To this end, a hybrid method, which allows us to transform problem (MP) into a scalar convex polynomial optimization…
Binary optimization is a central problem in mathematical optimization and its applications are abundant. To solve this problem, we propose a new class of continuous optimization techniques which is based on Mathematical Programming with…
In a multiobjective optimization problem a solution is called Pareto-optimal if no criterion can be improved without deteriorating at least one of the other criteria. Computing the set of all Pareto-optimal solutions is a common task in…
We consider multi-task learning, which simultaneously learns related prediction tasks, to improve generalization performance. We factorize a coefficient matrix as the product of two matrices based on a low-rank assumption. These matrices…
This work studies the behavior of three elitist multi- and many-objective evolutionary algorithms generating a high-resolution approximation of the Pareto optimal set. Several search-assessment indicators are defined to trace the dynamics…