• LAGRANGIAN DUALITY AND SADDLE POINT OPTIMALITY CONDITIONS OF ROUGH NONLINEAR OPTIMIZATION PROBLEM WHEN ROUGHNESS IN THE FEASIBLE REGION

Abstract

Deriving the dual of nonlinear optimization problem often yields a new insight into the nonlinear optimization problem at hand. The new insight may lead to simple techniques for solving the nonlinear problem. This paper presents duality theorems and saddle point optimality conditions of nonlinear optimization problem in rough environment when the objective function is deterministic function and roughness is in the feasible region. The concepts of duality and saddle point in the rough environment are discussed. Numerical examples are given to clarify the developed theory.