A “Joint+Marginal” Approach in Optimization

Chapter
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 166)

Abstract

We present the “joint+marginal” approach initially developed for polynomial optimization. In particular, it is shown that the optimal value (a function of the parameters) can be approximated in a strong sense by polynomials via solving a hierarchy of semidefinite programs whose size depends on the degree of the polynomial approximant. We also show how to exploit this approximation property in other contexts, e.g., to provide (a) an algorithm for robust optimization (where the parameter is the robust decision) and (b), an iterative algorithm for non parametric optimization (where the parameter is the first coordinate x1 of the variable, then x2 after x1 has been calculated, etc.)

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.LAAS-CNRS and Institute of MathematicsUniversity of ToulouseToulouse Cédex 4France

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