Pseudoconvex Multiobjective Continuous-time Problems and Vector Variational ‎Inequalities

Subject Areas : International Journal of Industrial Mathematics

E. ‎Khakrah‎ ¹ , A. R. Razani ² , M. Oveisiha‎ ³

1 - Department of Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, Iran.
2 - Department of Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, Iran.
3 - Department of Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, Iran.

Received: 2017-07-11 Accepted : 2017-07-11 Published : 2017-07-01

Keywords: Multiobjective continuous-time, Generalized vector variational, Efficiency, Generalized ‎convexity.‎,

Abstract :

In this paper, the concept of pseudoconvexity and quasiconvexity for continuous~-time functions are studied and an equivalence condition for pseudoconvexity is obtained. Moreover, under pseudoconvexity assumptions, some relationships between Minty and Stampacchia vector variational inequalities and continuous-time programming problems are presented. Finally, some characterizations of the solution sets of a single-valued continuous-time programming problem are ‎obtained.‎