Characterization of efficient solutions for a class of PDE-constrained vector control problems

Savin Treanţă

doi:10.3934/naco.2019035

Article Contents

2020, Volume 10, Issue 1: 93-106. Doi: 10.3934/naco.2019035

This issue Previous Article Existence and iterative approximation method for solving mixed equilibrium problem under generalized monotonicity in Banach spaces Next Article Unified vector quasiequilibrium problems via improvement sets and nonlinear scalarization with stability analysis

Characterization of efficient solutions for a class of PDE-constrained vector control problems

Savin Treanţă

University Politehnica of Bucharest, Faculty of Applied Sciences, Department of Applied Mathematics, 313 Splaiul Independentei, 060042 Bucharest, Romania

Received: October 2018

Revised: March 2019

Published: March 2020

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Abstract

In this paper, we define a V-KT-pseudoinvex multidimensional vector control problem. More precisely, we introduce a new condition on the functionals which are involved in a multidimensional multiobjective (vector) control problem and we prove that a V-KT-pseudoinvex multidimensional vector control problem is characterized so that all Kuhn-Tucker points are efficient solutions. Also, the theoretical results derived in this paper are illustrated with an application.

Keywords:

Multidimensional vector control problem,
Kuhn-Tucker optimality conditions,
V-KT-pseudoinvexity,
multiple integral cost functional,
flow.

Mathematics Subject Classification: Primary: 26B25, 65K10, 90C29; Secondary: 90C30, 49K20, 46T20, 58J32.

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Figure 1. Graphical illustrations for x(t) and u(t)

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