A Spectral Bundle Method for Semidefinite Programming

A Parallel Implementation of the Spectral Bundle Method for Semidefinite Programming

The spectral bundle method with second-order information

The spectral bundle method was introduced by Helmberg and Rendl [13] to solve a class of eigenvalue optimization problems that is equivalent to the class of semidefinite programs with the constant trace property. We investigate the feasibility and effectiveness of including full or partial second-order information in the spectral bundle method, building on work of Overton and Womersley [20, 23]...

An inexact spectral bundle method for convex quadratic semidefinite programming

We present an inexact spectral bundle method for solving convex quadratic semidefinite optimization problems. This method is a first-order method, hence requires much less computational cost each iteration than second-order approaches such as interior-point methods. In each iteration of our method, we solve an eigenvalue minimization problem inexactly, and solve a small convex quadratic semidef...

Incorporating Inequality Constraints in the Spectral Bundle Method

Semidefinite relaxations of quadratic 0-1 programming or graph partitioning problems are well known to be of high quality. However, solving them by primal-dual interior point methods can take much time even for problems of moderate size. Recently we proposed a spectral bundle method that allows to compute, within reasonable time, approximate solutions to structured, large equality constrained s...

Eigenvalue Optimization for Solving the MAX-CUT Problem

The purpose of this semester project is to investigate the Spectral Bundle Method, which is a specialized subgradient method particularly suited for solving large scale semidefinite programs that can be cast as eigenvalue optimization problems of the form min y∈R aλmax(C − m ∑ i=1 Aiyi) + b T y, where C and Ai are given real symmetric matrices, b ∈ R allows to specify a linear cost term, and a ...