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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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 |
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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: | |
URI: | https://livrepository.liverpool.ac.uk/id/eprint/3172185 |