Minimization methods for non-differentiable functions
Minimization methods for non-differentiable functions
Practical methods of optimization; (2nd ed.)
Practical methods of optimization; (2nd ed.)
A dual method for certain positive semidefinite quadratic programming problems
SIAM Journal on Scientific and Statistical Computing
Proximity control in bundle methods for convex
Mathematical Programming: Series A and B
Modern heuristic techniques for combinatorial problems
Modern heuristic techniques for combinatorial problems
Convergence of some algorithms for convex minimization
Mathematical Programming: Series A and B - Special issue: Festschrift in Honor of Philip Wolfe part II: studies in nonlinear programming
New variants of bundle methods
Mathematical Programming: Series A and B
Complexity estimates of some cutting plane methods based on the analytic barrier
Mathematical Programming: Series A and B
A quasi-second-order proximal bundle algorithm.
Mathematical Programming: Series A and B
SIAM Review
Variable metric bundle methods: from conceptual to implementable forms
Mathematical Programming: Series A and B - Special issue on computational nonsmooth optimization
Solving semidefinite quadratic problems within nonsmooth optimization algorithms
Computers and Operations Research
Primal-dual interior-point methods
Primal-dual interior-point methods
A bundle-Newton method for nonsmooth unconstrained minimization
Mathematical Programming: Series A and B
The Efficiency of Ballstep Subgradient Level Methods for Convex Optimization
Mathematics of Operations Research
Efficiency of proximal bundle methods
Journal of Optimization Theory and Applications
Convex analysis and variational problems
Convex analysis and variational problems
Nonsmooth algorithms to solve semidefinite programs
Advances in linear matrix inequality methods in control
Optimization by Vector Space Methods
Optimization by Vector Space Methods
Quasi-Newton Bundle-Type Methods for Nondifferentiable Convex Optimization
SIAM Journal on Optimization
On $\mathcalVU$-theory for Functions with Primal-Dual Gradient Structure
SIAM Journal on Optimization
A Globally and Superlinearly Convergent Algorithm for Nonsmooth Convex Minimization
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
A global progressive register allocator
Proceedings of the 2006 ACM SIGPLAN conference on Programming language design and implementation
A faster branch-and-bound algorithm for the test-cover problem based on set-covering techniques
Journal of Experimental Algorithmics (JEA)
A bundle-type algorithm for routing in telecommunication data networks
Computational Optimization and Applications
Dual decomposition for parsing with non-projective head automata
EMNLP '10 Proceedings of the 2010 Conference on Empirical Methods in Natural Language Processing
A Redistributed Proximal Bundle Method for Nonconvex Optimization
SIAM Journal on Optimization
Dual decomposition for natural language processing
HLT '11 Proceedings of the 49th Annual Meeting of the Association for Computational Linguistics: Tutorial Abstracts of ACL 2011
Exact decoding of phrase-based translation models through Lagrangian relaxation
EMNLP '11 Proceedings of the Conference on Empirical Methods in Natural Language Processing
Structured Learning and Prediction in Computer Vision
Foundations and Trends® in Computer Graphics and Vision
Journal of Artificial Intelligence Research
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Lagrangian relaxation is a tool to find upper bounds on a given (arbitrary) maximization problem. Sometimes, the bound is exact and an optimal solution is found. Our aim in this paper is to review this technique, the theory behind it, its numerical aspects, its relation with other techniques such as column generation.