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In this article, we derive an iterative scheme through a quasi-Newton technique to capture robust weakly efficient points of uncertain multiobjective optimization problems under the upper set less relation. It is assumed that the set of…

Optimization and Control · Mathematics 2025-05-21 K. Gupta , D. Ghosh , C. Tammer , X. Zhao , J. C. Yao

We define w-invex set, w-preinvex, w-strictly preinvex, w-quasi preinvex, w-strictly quasi preinvex, w-semi-strictly quasi preinvex, and w-pre pseudo-invex functions in this context. And these form a class of real functions, which is the…

Optimization and Control · Mathematics 2022-08-23 Musavvir Ali , Ehtesham Akhter

In classic robust optimization, it is assumed that a set of possible parameter realizations, the uncertainty set, is modeled in a previous step and part of the input. As recent work has shown, finding the most suitable uncertainty set is in…

Optimization and Control · Mathematics 2016-10-18 André Chassein , Marc Goerigk

We consider relative or subjective optimization problems where the goal function and feasible set are dependent of the current state of the system under consideration. In general, they are formulated as quasi-equilibrium problems, hence…

Optimization and Control · Mathematics 2020-03-19 I. V. Konnov

In this paper, we propose a new Fully Composite Formulation of convex optimization problems. It includes, as a particular case, the problems with functional constraints, max-type minimization problems, and problems of Composite…

Optimization and Control · Mathematics 2021-03-24 Nikita Doikov , Yurii Nesterov

We study the problem of minimizing a nonnegative separable concave function over a compact feasible set. We approximate this problem to within a factor of 1+epsilon by a piecewise-linear minimization problem over the same feasible set. Our…

Optimization and Control · Mathematics 2012-01-17 Thomas L. Magnanti , Dan Stratila

Decomposition techniques for linear programming are difficult to extend to conic optimization problems with general non-polyhedral convex cones because the conic inequalities introduce an additional nonlinear coupling between the variables.…

Optimization and Control · Mathematics 2013-06-04 Yifan Sun , Martin S. Andersen , Lieven Vandenberghe

We consider the problem of approximating the solution of variational problems subject to the constraint that the admissible functions must be convex. This problem is at the interface between convex analysis, convex optimization, variational…

Numerical Analysis · Mathematics 2015-03-19 Adam M. Oberman

In this paper, we provide a new scheme for approximating the weakly efficient solution set for a class of vector optimization problems with rational objectives over a feasible set defined by finitely many polynomial inequalities. More…

Optimization and Control · Mathematics 2022-05-26 Feng Guo , Liguo Jiao

Combinatorial optimization can be described as the problem of finding a feasible subset that maximizes a objective function. The paper discusses combinatorial optimization problems, where for each dimension the set of feasible subsets is…

Computational Complexity · Computer Science 2024-11-27 Nimrod Megiddo

We introduce a class of stochastic algorithms for minimizing weakly convex functions over proximally smooth sets. As their main building blocks, the algorithms use simplified models of the objective function and the constraint set, along…

Optimization and Control · Mathematics 2025-01-22 Damek Davis , Dmitriy Drusvyatskiy , Zhan Shi

This paper studies approximate solutions of a linear fractional vector optimization problem without requiring boundedness of the constraint set. We establish necessary and sufficient conditions for approximating weakly efficient points of…

Optimization and Control · Mathematics 2024-12-12 Nguyen Thi Thu Huong

We suggest an adaptive version of a partial linearization method for composite optimization problems. The goal function is the sum of a smooth function and a non necessary smooth convex separable function, whereas the feasible set is the…

Optimization and Control · Mathematics 2016-05-26 I. V. Konnov

This paper presents a piecewise convexification method to approximate the whole approximate optimal solution set of non-convex optimization problems with box constraints. In the process of box division, we first classify the sub-boxes and…

Optimization and Control · Mathematics 2022-06-30 Qiao Zhu , Liping Tang , Xinmin Yang

In this paper we deal with the feasibility-seeking problem for unions of convex sets (UCS) sets and propose an iterative process for its solution. Renewed interest in this problem stems from the fact that it was recently discovered to serve…

Optimization and Control · Mathematics 2025-04-08 Yair Censor , Alexander J. Zaslavski

This paper presents a convex optimization-based method for finding the globally optimal solutions of a class of mixed-integer non-convex optimal control problems. We consider problems that are non-convex in the input norm, which is a…

Optimization and Control · Mathematics 2019-11-20 Danylo Malyuta , Michael Szmuk , Behcet Acikmese

We study rigidity/flexibility properties of global solutions to the thin obstacle problem. For solutions with bounded positive sets, we give a classification in terms of their expansions at infinity. For solutions with bounded contact sets,…

Analysis of PDEs · Mathematics 2025-05-01 Xavier Fernández-Real , Hui Yu

There are different solution concepts for convex vector optimization problems (CVOPs) and a recent one, which is motivated from a set optimization point of view, consists of finitely many efficient solutions that generate polyhedral inner…

Optimization and Control · Mathematics 2019-05-28 Firdevs Ulus

Conic optimization has recently emerged as a powerful tool for designing tractable and guaranteed algorithms for non-convex polynomial optimization problems. On the one hand, tractability is crucial for efficiently solving large-scale…

In this paper, we investigate the nonemptiness of weak Pareto efficient solution set for a class of nonsmooth vector optimization problems on a nonempty closed constraint set without any boundedness and convexity assumptions. First, we…

Optimization and Control · Mathematics 2024-08-09 Danyang Liu , Jun Li , Giandomenico Mastroeni