Approximations in proximal bundle methods and decomposition of convex programs

Journal of Optimization Theory and Applications

Volumn 84, Issue 3, 1995, Pages 529-548

  Kiwiel, K C ^a  

^a SYSTEMS RESEARCH INSTITUTE   (Poland)

Author keywords

convex programming; decomposition; large scale programming; Nondifferentiable optimization; nonsmooth optimization; proximal bundle methods

Indexed keywords

EID: 21844495838     PISSN: 00223239     EISSN: 15732878     Source Type: Journal    
DOI: 10.1007/BF02191984     Document Type: Article

References (33)

1. Proximity Control in Bundle Methods for Convex Nondifferentiable Minimization
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3. Exact Penalty Functions in Proximal Bundle Methods for Constrained Convex Nondifferentiable Minimization
4. On the Douglas-Rachford Splitting Method and the Proximal Point Algorithm for Maximal Monotone Operators
5. Lagrangian Decomposition and Nonsmooth Optimization: Bundle Algorithm, Prox Iteration, Augmented Lagrangian
6. A Class of Convergent Primal-Dual Subgradient Algorithms for Decomposable Convex Programs
7. A Primal-Dual Conjugate Subgradient Algorithm for Specially Structured Linear and Convex Programming Problems
8. Applications of the Method of Partial Inverses to Convex Programming: Decomposition
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10. Applications of a Splitting Algorithm to Decomposition in Convex Programming and Variational Inequalities
11. Decomposition Principle for Linear Programs
12. A General Approach to Decomposition of Optimization Systems
13. Monotone Operators and the Proximal Point Algorithm
14. Convergence of Some Algorithms for Convex Minimization
15. An Algorithm for Nonsmooth Convex Minimization with Errors
16. An Application of the ∈-Subgradient Method to the Solution of the Dual and Primal Problems of Convex Programming
17. Bundle-Based Decomposition: Description and Preliminary Results
18. Bundle-Based Decomposition: Conditions for Convergence
19. Approximations in Decomposition of Large-Scale Convex Programs via a Nondifferentiable Optimization Method
20. A Version of the Bundle Idea for Minimizing a Nonsmooth Function: Conceptual Idea, Convergence Analysis, Numerical Results
21. A Dual Method for Certain Positive-Semidefinite Quadratic Programming Problems
22. A Cholesky Dual Method for Proximal Piecewise Linear Programming
23. Numerical Experiments in Nonsmooth Optimization
24. A Method for Solving Certain Quadratic Programming Problems Arising in Nonsmooth Optimization