Lagrangian Relaxation

@inproceedings{Lemarchal2001LagrangianR,
  title={Lagrangian Relaxation},
  author={C. Lemar{\'e}chal},
  booktitle={Computational Combinatorial Optimization},
  year={2001}
}
  • C. Lemaréchal
  • Published in
    Computational Combinatorial…
    2001
  • Computer Science, Mathematics
  • 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. 
    305 Citations
    Improved Lagrangian bounds and heuristics for the generalized assignment problem
    • 1
    • PDF
    A Lagrangian bound for many-to-many assignment problems
    • 16
    • Highly Influenced
    • PDF
    On a primal-proximal heuristic in discrete optimization
    • 21
    The omnipresence of Lagrange
    • 37
    Lagrangian heuristic for a class of the generalized assignment problems
    • 11
    • PDF

    References

    SHOWING 1-10 OF 77 REFERENCES
    Semidefinite Relaxations and Lagrangian Duality with Application to Combinatorial Optimization
    • 84
    • PDF
    Convergence of some algorithms for convex minimization
    • 236
    A geometric study of duality gaps, with applications
    • 82
    A Dual Method for Certain Positive Semidefinite Quadratic Programming Problems
    • 46
    Dual Applications of Proximal Bundle Methods, Including Lagrangian Relaxation of Nonconvex Problems
    • 99
    • PDF
    A recipe for semidefinite relaxation for (0,1)-quadratic programming
    • 207
    • PDF
    Letter to the Editor - A Note on Cutting-Plane Methods Without Nested Constraint Sets
    • 19
    On improving relaxation methods by modified gradient techniques
    • 273
    Generalized Linear Programming Solves the Dual
    • 75
    • PDF
    Interior Point Methods in Semidefinite Programming with Applications to Combinatorial Optimization
    • F. Alizadeh
    • Mathematics, Computer Science
    • SIAM J. Optim.
    • 1995
    • 942
    • PDF