Optimality Conditions for Semi-infinite and Generalized Semi-infinite Programs via lp Exact Penalty Functions
نویسندگان
چکیده
In this paper, we will study optimality conditions of semi-infinite programs and generalized semi-infinite programs, for which the gradient objective function when evaluated at any feasible direction for the linearized constraint set is non-negative. We consider three types of penalty functions for semi-infinite program and investigate the relationship among the exactness of these penalty functions. We employ lower order integral exact penalty functions and the second-order generalized derivative of the constraint function to establish optimality conditions for semi-infinite programs. We adopt the exact penalty function technique in terms of a classical augmented Lagrangian function for the lower level problems of generalized semiinfinite programs to transform them into an semi-infinite programs and then apply our results for semi-infinite programs to derive the optimality condition for generalized semi-infinite programs. We will give various examples to illustrate our results and assumptions.
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