Duality for multiobjective variational control problems with \((\Phi, \rho)\)-invexity
The author considers a variational (multiobjective) control problem. In order to formulate a strong duality theorem, he gives the Karush-Kuhn-Tucker necessary optimality conditions for the considered multiobjective variational control problem (MVPP). The concept of \((\Phi, \rho)\)-invexity is extended to multiobjective variational control problems. The concept of efficiency is used to formulate an MV control dual problem in the sense of Mond-Weir and in the sense of Wolfe for the considered MVPP. Under \((\Phi, \rho)\)-invexity assumptions imposed on the functions involved in the considered multiobjective variational control problem, weak, strong, converse and strict converse dual theorems in the sense of Mond-Weir and in the sense of Wolfe are proved between the new class of multiobjective variational control problems and their duals.
Karush-Kuhn-Tucker optimality conditions
multiobjective variational control problems
scientific article; zbMATH DE number 6418677