Lagrange multipliers saddle points and scalarizations in composite multiobjective nonsmooth programming

Abstract

A Lagrange multiplier theorem is established for a nonsmooth constrained multiobjective optimizatioi problems where the objective function and the constraints are compositions of F-invex functions, anc locally Lipschitz and Gateaux differentiable functions. Furthermore, a vector valued Lagrangian is intro duced and vector valued saddle point results are presented. A scalarization result and a characterizatior of the set of all conditionally properly efficient solutions for V-invex composite problems are alsc discussed under appropriate conditions.

Keywords:

• Composite Functions
• Nonsmooth Programming
• Multiobjective Problems
• Lagrangc Multipliers
• Saddle Points
• Scalarizations