Chapter 5 Parametric Polynomial Optimization

Abstract

Roughly speaking, given a set of parameters Y and an optimization problem whose description depends on $y \in Y$ (call it P _y), parametric optimization is concerned with the behavior and properties of the optimal value as well as primal (and possibly dual) optimal solutions of P _y, when y varies in Y. This is a quite challenging problem for which in general only local information around some nominal value y0 of the parameter can be obtained. Sometimes, in the context of optimization with data uncertainty, some probability distribution on the parameter set Y is available and in this context one is also interested in, e.g., the distributions of the optimal value and optimal solutions, all viewed as random variables.