Article Abstract:
The subgradient projection method turns in a better performance than traditional subgradient optimization. This indicates that generalizing the subgradient optimization method for nondifferentiable convex programming to utilize conditional subgradients is effective in improving subgradient optimization schemes. It was applied in three areas, namely, uncapacitated facility location, two-person zero-sum matrix games and multicommodity network flows to examine its efficacy. The finding that it performs better than traditional subgradient optimization is significant since these schemes are widely used in Lagrangean relaxation.
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Article Abstract:
The method of exponential smoothing facilitates the convergence of subgradient optimization for a class of generalized assignment problems and capacitated warehouse location problems. It can also be used for other combinatorial optimization problems which could result to earlier fathoming in branch and bound algorithms. Its use opens a possibility that the effectiveness of Lagrangean heuristics can be enhanced.
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Article Abstract:
The new convergence results for conditional epselon-subgradient algorithms for general convex programs are reported. The application of this technique to solve non-strictly convex-concave saddle point problems, such as primal-dual formulations of linear programs is established.
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