Necessary optimality conditions in problems involving set-valued maps with parameters. (Q696132)

The authors study a parametric vector optimization problem in which the objective function and the constraints are given by set-valued maps. Under a rather weak convexity assumption and a differentiability hypothesis, they establish necessary criteria for local weak optimal solutions and local solutions. These criteria generalize those of the authors' earlier paper [ibid. 25, No. 2, 125--136 (2000; Zbl 1073.90547)] in which the equality constraint was supposed to be single-valued.