Hartley Proper Efficiency in Multiobjective Optimization Problems with Locally Lipschitz Set-valued Objectives and Constraints

In this paper we give necessary conditions for Hartley proper efficiency in a vector optimization problem whose objectives and constraints are described by nonconvex locally Lipchitz set-valued maps. The obtained necessary conditions are written in terms of a Lagrange multiplier rule. Our approach is based on a reduction theorem which leads the problem of studying proper efficiency to a scalar optimization problem whose objective is given by a function of max-type. Sufficient conditions for Hartley proper efficiency are also considered.