A “Joint+Marginal” Approach in Optimization

Jean B. Lasserre ()
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Jean B. Lasserre: University of Toulouse

Chapter Chapter 10 in Handbook on Semidefinite, Conic and Polynomial Optimization, 2012, pp 271-295 from Springer

Abstract: 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.)

Keywords: Knapsack Problem; Semidefinite Program; Polynomial Optimization; Real Symmetric Matrix; Semidefinite Relaxation (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:spr:isochp:978-1-4614-0769-0_10

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DOI: 10.1007/978-1-4614-0769-0_10

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