Convergence of the mixing method

An iterative algorithm for solving diagonally constrained semidefinite programs

Master thesis (2022)

Authors

D.S.L. Eelkema Electrical Engineering, Mathematics and Computer Science

Contributors

D. de Laat Discrete Mathematics and Optimization - EEMCS (supervisor 1)
Faculty
Electrical Engineering, Mathematics and Computer Science
Copyright: © 2022 Dominic Eelkema
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Published Date

26-09-2022

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Abstract

This thesis explores the convergence of the mixing method, an iter- ative algorithm for solving diagonally constrained semidefinite programs. In this paper we first give an exposition of the convergence proof for the mixing method based on the proof by Wang, Chang, and Kolter , where we restructure some parts of the proof and provide extra de- tails. Then we construct an example where the linear convergence rate of the mixing method is close to one when near the optimal solution. The mixing method is then compared for convergence speed to a semidefinite programming solver and gradient descent on random max-cut instances. For instances of the max-cut, it is found that the mixing method outper- forms other methods.