Continuity of the Optimal Value Function Under the Mangasarian-Fromovitz Constraint Qualification

摘要

We demonstrate the continuity of the optimal value of general inequality-constrained parametric nonlinear programs having a solution point that satisfies the Mangasarian-Fromovitz Constraint Qualification (MFCQ). This result is applied to prove the continuity of the optimal value function for general inequality-equality parametric programs under MFCQ, by using a variable reduction approach. An abstract set (not defined by functional inequalities or equalities) is allowed to enter (nontrivially into the definition of the feasible region and results regarding the behavior of the parameter dependent feasible region and solution set are also obtained. (Author)