Decomposition of structured large-scale optimization problems and parallel optimization

Thesis/Dissertation · Thu Jan 01 04:00:00 EST 1987

OSTI ID:7183792

Medhi, D

Block-angular linear-programming problems and linear multi-commodity network optimization problems can be cast into a form given. In the approach, the Rockafellar dual of the problem is taken to arrive at an unconstrained nonsmooth maximization problem. The difficulty arises from the non-smoothness of the dual objective. Traditional subgradient methods are not good enough as they do not have implementable stopping criteria and are reported to have slow convergence. One also may not obtain a primal solution at the end. Instead, a modified bundle algorithm is applied that has an implementable stopping criterion, and more importantly, one can recover an approximate primal solution. Some theoretical a posteriori error information on the approximate solution is also obtained. This algorithm is implemented on randomly generated block-angular linear-programming problems of size up to 4000 equality constraints and 10,000 variables. The implementation ran up to seventy times faster than MINOS version 5.0, and did substantially better than an advanced implementation of the Dantzig-Wolfe decomposition method. For this type of problem, the algorithm appears very promising.

• Research Organization: Wisconsin Univ., Madison (USA)
• OSTI ID: 7183792
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
990210* -- Supercomputers-- (1987-1989)
ALGORITHMS
COMPUTER NETWORKS
ERRORS
LINEAR PROGRAMMING
MATHEMATICAL LOGIC
OPTIMIZATION
PARALLEL PROCESSING
PROGRAMMING