On the numerical treatment of a class of semi-infinite terminal problems^∗

^∗Partially supported by the German Research Society (DFG)

^∗Partially supported by the german research society (DFG)$ef:

Abstract

A new class of nonlinear programming problems is considered with an infinite family of constraints, depending on a parameter. The maximal value of this parameter, for which the constraints remain compatible, has to be sought

The problems studied are, in general, ill-posed. Their solvability and some properties of the solutions are briefly described and a solution method is suggested

The use of the proximal point approach coupled with a successive discretization of the original problem ensures well-posedness of the auxiliary problems. Due to regularization an efficient deleting rule is applicable, which excludes an essential part of the constraints in the discretized problems. Conditions guaranteeing convergence of the iterates to some solution of the problem are established

Some numerical examples are presented showing the behavior of the method

Keywords:

• Semi-Infinite Optimization
• Ill-Posed Problems
• Proximal Methods

^∗Partially supported by the German Research Society (DFG)

^∗Partially supported by the German Research Society (DFG)

Notes

^∗Partially supported by the German Research Society (DFG)