Proximity control in bundle methods for convex
Mathematical Programming: Series A and B
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Rank-Two Relaxation Heuristics for MAX-CUT and Other Binary Quadratic Programs
SIAM Journal on Optimization
Solving Large-Scale Sparse Semidefinite Programs for Combinatorial Optimization
SIAM Journal on Optimization
A Spectral Bundle Method for Semidefinite Programming
SIAM Journal on Optimization
Dual Applications of Proximal Bundle Methods, Including Lagrangian Relaxation of Nonconvex Problems
SIAM Journal on Optimization
Relaxation and Decomposition Methods for Mixed Integer Nonlinear Programming (International Series of Numerical Mathematics)
On greedy construction heuristics for the MAX-CUT problem
International Journal of Computational Science and Engineering
A discrete filled function algorithm for approximate global solutions of max-cut problems
Journal of Computational and Applied Mathematics
Global optimality conditions and optimization methods for quadratic integer programming problems
Journal of Global Optimization
A new discrete filled function method for solving large scale max-cut problems
Numerical Algorithms
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This paper presents a smoothing heuristic for an NP-hard combinatorial problem. Starting with a convex Lagrangian relaxation, a pathfollowing method is applied to obtain good solutions while gradually transforming the relaxed problem into the original problem formulated with an exact penalty function. Starting points are drawn using different sampling techniques that use randomization and eigenvectors. The dual point that defines the convex relaxation is computed via eigenvalue optimization using subgradient techniques.The proposed method turns out to be competitive with the most recent ones. The idea presented here is generic and can be generalized to all box-constrained problems where convex Lagrangian relaxation can be applied. Furthermore, to the best of our knowledge, this is the first time that a Lagrangian heuristic is combined with pathfollowing techniques.