Titlebook: Handbook on Semidefinite, Conic and Polynomial Optimization; Miguel F. Anjos,Jean B. Lasserre Book 2012 Springer Science+Business Media, L

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Convex Hulls of Algebraic Setser the reals. The method relies on sums of squares of polynomials and the dual theory of moment matrices. The main feature of the technique is that all computations are done modulo the ideal generated by the polynomials defining the set to the convexified. This work was motivated by questions raised

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A “Joint+Marginal” Approach in Optimizationn 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

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An Introduction to Formally Real Jordan Algebras and Their Applications in Optimizationnvex optimization problems, such as complementarity and interior point algorithms, give rise to algebraic questions. Next we study the basic properties of formally real Jordan algebras including properties of their multiplication operator, quadratic representation, spectral properties and Peirce dec

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Complementarity Problems Over Symmetric Cones: A Survey of Recent Developments in Several Aspects of researchers in the last decade. Many of studies done on the SCCP can be categorized into the three research themes, interior point methods for the SCCP, merit or smoothing function methods for the SCCP, and various properties of the SCCP. In this paper, we will provide a brief survey on the rece

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Self-Regular Interior-Point Methods for Semidefinite Optimization choice to solve them. This chapter reviews the fundamental concepts and complexity results of Self-Regular (SR) IPMs for semidefinite optimizaion, that up to a log factor achieve the best polynomial complexity bound of small neighborhood IPMs. SR kernel functions are in the core of SR-IPMs. This ch