Connections between Non-Linear Optimization Problems and Associated Variational Inequalities

Savin Treanţă (), Tadeusz Antczak and Tareq Saeed
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Savin Treanţă: Department of Applied Mathematics, University Politehnica of Bucharest, 060042 Bucharest, Romania
Tadeusz Antczak: Faculty of Mathematics and Computer Science, University of Lodz, Banacha 22, 90-238 Lodz, Poland
Tareq Saeed: Financial Mathematics and Actuarial Science (FMAS)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

Mathematics, 2023, vol. 11, issue 6, 1-12

Abstract: In this paper, by using the invexity (or pseudoinvexity) and Fréchet differentiability of some integral functionals of curvilinear type, we state some relations between the solutions of a new non-linear optimization problem and the associated variational inequality. In order to prove the results derived in this paper, we use the new notion of invex set by considering some given functions. To justify the effectiveness and outstanding applicability of this work, some illustrative examples are provided.

Keywords: multiple objective optimization; invex set; integral functional; Fréchet differentiability; invexity; pseudoinvexity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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