Interior-Point Algorithms for Semidefinite Programming Based on a Nonlinear Formulation
Computational Optimization and Applications
A Note on the Calculation of Step-Lengths in Interior-Point Methods for Semidefinite Programming
Computational Optimization and Applications
Cutting Plane Algorithms for Nonlinear Semi-Definite Programming Problems with Applications
Journal of Global Optimization
Computational Combinatorial Optimization, Optimal or Provably Near-Optimal Solutions [based on a Spring School]
Semidefinite programming for discrete optimization and matrix completion problems
Discrete Applied Mathematics
The bundle method for hard combinatorial optimization problems
Combinatorial optimization - Eureka, you shrink!
Computational Optimization and Applications
A low-level hybridization between memetic algorithm and VNS for the max-cut problem
GECCO '05 Proceedings of the 7th annual conference on Genetic and evolutionary computation
Lagrangian Smoothing Heuristics for Max-Cut
Journal of Heuristics
On Extracting Maximum Stable Sets in Perfect Graphs Using Lovász's Theta Function
Computational Optimization and Applications
Fast SDP Relaxations of Graph Cut Clustering, Transduction, and Other Combinatorial Problems
The Journal of Machine Learning Research
A semidefinite programming-based heuristic for graph coloring
Discrete Applied Mathematics
Algorithm 875: DSDP5—software for semidefinite programming
ACM Transactions on Mathematical Software (TOMS)
Local convergence of an augmented Lagrangian method for matrix inequality constrained programming
Optimization Methods & Software
Optimization Methods & Software
Hybridizing the cross-entropy method: An application to the max-cut problem
Computers and Operations Research
Improved spectral relaxation methods for binary quadratic optimization problems
Computer Vision and Image Understanding
Advanced Scatter Search for the Max-Cut Problem
INFORMS Journal on Computing
A second-order cone cutting surface method: complexity and application
Computational Optimization and Applications
Competitive simulated annealing and Tabu Search algorithms for the max-cut problem
Proceedings of the 11th Annual conference on Genetic and evolutionary computation
Local search starting from an LP solution: Fast and quite good
Journal of Experimental Algorithmics (JEA)
Provably near-optimal solutions for very large single-row facility layout problems
Optimization Methods & Software - GLOBAL OPTIMIZATION
A parallel interior point decomposition algorithm for block angular semidefinite programs
Computational Optimization and Applications
LSMS'07 Proceedings of the Life system modeling and simulation 2007 international conference on Bio-Inspired computational intelligence and applications
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
Journal of Global Optimization
Solving the maxcut problem by the global equilibrium search
Cybernetics and Systems Analysis
Knapsack problem with probability constraints
Journal of Global Optimization
Using landscape measures for the online tuning of heterogeneous distributed gas
Proceedings of the 13th annual conference companion on Genetic and evolutionary computation
A local genetic algorithm for binary-coded problems
PPSN'06 Proceedings of the 9th international conference on Parallel Problem Solving from Nature
A cutting planes algorithm based upon a semidefinite relaxation for the quadratic assignment problem
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Distance metric learning with eigenvalue optimization
The Journal of Machine Learning Research
Expert Systems with Applications: An International Journal
A hybridization between memetic algorithm and semidefinite relaxation for the max-cut problem
Proceedings of the 14th annual conference on Genetic and evolutionary computation
A new discrete filled function method for solving large scale max-cut problems
Numerical Algorithms
An inexact spectral bundle method for convex quadratic semidefinite programming
Computational Optimization and Applications
Path Relinking Scheme for the Max-Cut Problem within Global Equilibrium Search
International Journal of Swarm Intelligence Research
Max-k-Cut by the Discrete Dynamic Convexized Method
INFORMS Journal on Computing
Breakout local search for the vertex separator problem
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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A central drawback of primal-dual interior point methods for semidefinite programs is their lack of ability to exploit problem structure in cost and coefficient matrices. This restricts applicability to problems of small dimension. Typically, semidefinite relaxations arising in combinatorial applications have sparse and well-structured cost and coefficient matrices of huge order. We present a method that allows us to compute acceptable approximations to the optimal solution of large problems within reasonable time.Semidefinite programming problems with constant trace on the primal feasible set are equivalent to eigenvalue optimization problems. These are convex nonsmooth programming problems and can be solved by bundle methods. We propose replacing the traditional polyhedral cutting plane model constructed from subgradient information by a semidefinite model that is tailored to eigenvalue problems. Convergence follows from the traditional approach but a proof is included for completeness. We present numerical examples demonstrating the efficiency of the approach on combinatorial examples.