Self-Regular Interior-Point Methods for Semidefinite Optimization

Maziar Salahi () and Tamás Terlaky ()
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Maziar Salahi: University of Guilan
Tamás Terlaky: Lehigh University

Chapter Chapter 15 in Handbook on Semidefinite, Conic and Polynomial Optimization, 2012, pp 437-454 from Springer

Abstract: Abstract Semidefinite optimization has an ever growing family of crucial applications, and large neighborhood interior point methods (IPMs) yield the method of 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 chapter reviews several none SR kernel functions too. IPMs based on theses kernel functions enjoy similar iteration complexity bounds as SR-IPMs, though their complexity analysis requires additional tools.

Keywords: Semidefinite Optimization (SDO); Interior Point Methods (IPMs); Worst-case Iteration Complexity; Eligible Kernel Functions; Second-order Cone Optimization (SOCO) (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/978-1-4614-0769-0_15

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