On the structure of optimal solutions in a mathematical programming problem in a convex space

Piunovskiy, Alexey ORCID: 0000-0002-9683-4856 and Zhang, Yi ORCID: 0000-0002-3200-6306 (2023) On the structure of optimal solutions in a mathematical programming problem in a convex space. Operations Research Letters, 51 (5). pp. 488-493.

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Official URL: http://dx.doi.org/10.1016/j.orl.2023.07.006

Abstract

We consider an optimization problem in a convex space E with an affine objective function, subject to J affine constraints, where J is a given nonnegative integer. We apply the Feinberg-Shwartz lemma in finite dimensional convex analysis to show that there exists an optimal solution, which is in the form of a convex combination of no more than J+1 extreme points of E. The concerned problem does not seem to fit into the framework of standard convex optimization problems.

Item Type:	Article
Uncontrolled Keywords:	Feinberg-Shwartz lemma, Extreme point, Mixed optimal solution, Problem with constraints
Divisions:	Faculty of Science and Engineering > School of Physical Sciences
Depositing User:	Symplectic Admin
Date Deposited:	14 Aug 2023 07:14
Last Modified:	16 Nov 2023 22:16
DOI:	10.1016/j.orl.2023.07.006
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3172185