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

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.

Solving invex multitime control problems with first‐order PDE constraints via the absolute value exact penalty method

“…This is a consequence of various applications of multitime control optimization problems with first‐order PDE constraints in many areas of human activity in which modern man lives and works, for example, in economics, mechanics, engineering, physics, and others. Therefore, the aforementioned control optimization problems have been intensively studied in the literature in the last few years (see, e.g., References 1–9, and others).…”

On Some Constrained Optimization Problems

“…By considering the three major approaches (variational calculus, the Pontryagin maximum principle, and dynamic programming) associated with the optimal control theory, many researchers have investigated certain controlled processes in nature using some functionals with ODE/PDE or mixed constraints. In this regard, Treanţȃ [1][2][3], Jayswal et al [4], and Mititelu and Treanţȃ [5] studied some classes of optimization problems defined by integral functionals of multiple and/or path-independent curvilinear type, having various constraints involving first-order partial differential equations and inequations. Schmitendorf [6], by transforming the considered control problems into the standard form and then using Pontryagin's principle, formulated necessary conditions of optimality for a class of control problems subjected to isoperimetric constraints.…”

A necessary and sufficient condition of optimality for a class of multidimensional control problems

“…For instance, Arana‐Jiménez et al 5 and Oliveira et al 6 have extended the notion of KT‐invexity from mathematical programming to the classical optimal control problem. Recently, second‐order Karush‐Kuhn‐Tucker optimality conditions associated with multiobjective optimal control problems have been investigated by Kien et al 7 Furthermore, the concept of invexity has been extended to the multidimensional variational problems (see, quite recently, Mititelu and Treanţă, 8 Treanţă and Arana‐Jiménez, 9 Treanţă 10,11 ).…”