Lagrange multipliers saddle points and scalarizations in composite multiobjective nonsmooth programming

Abstract

A Lagrange multiplier theorem is established for a nonsmooth constrained multiobjective optimization problems where the objective function and the constraints are compositions of V-invex functions, and locally Lipschitz and Gåteaux differentiable functions. Furthermore, a vector valued Lagrangian is introduced and vector valued saddle point results are presented. A scalarization result and a characterization of the set of all conditionally properly efficient solutions for V-invex composite problems are also discussed under appropriate conditions.