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.
Original language | English |
---|---|
Pages (from-to) | 488-493 |
Number of pages | 6 |
Journal | Operations Research Letters |
Volume | 51 |
Issue number | 5 |
Early online date | 28 Jul 2023 |
DOIs | |
Publication status | Published - Sept 2023 |
Bibliographical note
Funding Information:We thank the anonymous referee for the careful reading and helpful remarks. In particular, Remark 2.1 is suggested by him/her.
Publisher Copyright:
© 2023 The Author(s)
Keywords
- Extreme point
- Feinberg-Shwartz lemma
- Mixed optimal solution
- Problem with constraints
ASJC Scopus subject areas
- Software
- Management Science and Operations Research
- Industrial and Manufacturing Engineering
- Applied Mathematics