An Introduction to Formally Real Jordan Algebras and Their Applications in Optimization

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

Abstract

In this chapter we study formally real Jordan algebras and their impact on certain convex optimization problems. We first show how common topics in convex 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 decomposition. Finally we show how this theory transparently unifies presentation and analysis of issues such as degeneracy and complementarity, and proofs of polynomial time convergence of interior point methods in linear, second order and semidefinite optimization problems.

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Rutgers Business School and RUTCORRutgers-State University of New JerseyPiscatawayUSA

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