ON DUALITY THEOREMS FOR ROBUST OPTIMIZATION PROBLEMS

A robust optimization problem, which has a maxi-mum function of continuously di？？erentiable functions as its objec- tive function, continuously di？？erentiable functions as its constraint functions and a geometric constraint, is considered. We prove a nec-essary optimality theorem and a su±cient optimality theorem for the robust optimization problem. We formulate a Wolfe type dual problem for the robust optimization problem, which has a di？？eren- tiable Lagrangean function, and establish the weak duality theorem and the strong duality theorem which hold between the robust opti-mization problem and its Wolfe type dual problem. Moreover, sad- dle point theorems for the robust optimization problem are given under convexity assumptions.