Parametric Approximation and Optimization

Abstract

This chapter discusses the parametric approximation and optimization and defines a family of semi-infinite minimization problems with family parameter and parameter space. A parametric linear optimization problem is described with variable matrix and variable restriction vector. Parametric linear finite optimization has many applications. The chapter proves an always sufficient criterion for a minimal point and introduces pointwise convex optimization problem. Many important optimization problems are pointwise convex, for example linear, convex, and fractional optimization problems. It is shown that if the minimum set mapping is upper semicontinuous, then at least one minimum point satisfies the criterion.