Continuous-Time Multiobjective Optimization Problems via Invexity

Abstract

We introduce some concepts of generalized invexity for the continuous-time multiobjective programming problems, namely, the concepts of Karush-Kuhn-Tucker invexity and Karush-Kuhn-Tucker pseudoinvexity. Using the concept of Karush-Kuhn-Tucker invexity, we study the relationship of the multiobjective problems with some related scalar problems. Further, we show that Karush-Kuhn-Tucker pseudoinvexity is a necessary and suffcient condition for a vector Karush-Kuhn-Tucker solution to be a weakly efficient solution.

On sufficient optimality conditions for multiobjective control problems

“…where the inequality, which follows from (19), the fact that (ν 0 , ν 1 ) ∈ N C (x(S),x(T )), (18) and (3), contradicts (20).…”

“…Now proceed as in the proof of Theorem 2, observing that (20) holds without any additional assumption, since g(x(S), X (T )) < g(x(S),x(T )) and 0 = ω ≥ 0, to get a contradiction.…”

New optimality conditions in vector continuous-time programming

“…Vector continuous-time programming problem has been the subject of numerous investigations in the past three decades. This problem was studied in [3,4,5,6]. In [4,5] a fundamental tool was Gordan's Transposition Theorem given in [7].…”

A Full Rank Condition for Continuous-Time Optimization Problems with Equality and Inequality Constraints

“…The same authors established KKT-invexity for nonsmooth continuoustime programming problems [9]. The multi-objective case was considered in [7]. de Oliveira [6] also studied multi-objective continuous-time programming problems, but without imposing any differentiability assumption.…”