Dual Applications of Proximal Bundle Methods, Including Lagrangian Relaxation of Nonconvex Problems

Authors:
Stefan Feltenmark;Krzysztof C. Kiwiel
Affiliations:
-;-
Venue:
SIAM Journal on Optimization
Year:
1999

Citing 0
Cited 5

Dual Bounds and Optimality Cuts for All-Quadratic Programs with Convex Constraints

Journal of Global Optimization
Bundle Methods in Stochastic Optimal Power Management: A Disaggregated Approach Using Preconditioners

Computational Optimization and Applications
Lagrangian Relaxation

Computational Combinatorial Optimization, Optimal or Provably Near-Optimal Solutions [based on a Spring School]
Lagrangian Smoothing Heuristics for Max-Cut

Journal of Heuristics
An Inexact Bundle Approach to Cutting-Stock Problems

INFORMS Journal on Computing

Quantified Score

Hi-index	0.00

Visualization

Abstract

We exhibit useful properties of proximal bundle methods for finding $\min_Sf$, where f and S are convex. We show that they asymptotically find objective subgradients and constraint multipliers involved in optimality conditions, multipliers of objective pieces for max-type functions, and primal and dual solutions in Lagrangian decomposition of convex programs. When applied to Lagrangian relaxation of nonconvex programs, they find solutions to relaxed convexified versions of such programs. Numerical results are presented for unit commitment in power production scheduling.