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An exponential-function reduction method for block-angular convex programs

Author: Michael D Grigoriadis; Leonid Khachiyan
Publisher: New Brunswick, N.J. : Rutgers University, Dept. of Computer Science, Laboratory for Computer Science Research, [1993]
Series: Rutgers University.; Department of Computer Science.; Laboratory for Computer Science Research.; Technical report
Edition/Format:   Book : EnglishView all editions and formats
Database:WorldCat
Summary:
Abstract: "An exponential potential-function reduction algorithm for convex block-angular optimization problems is described. These problems are characterized by K disjoint convex compact sets called blocks and M nonnegative-valued convex block-separable coupling inequalities with a nonempty interior. A given convex block-separable function is to be minimized. The method reduces the optimization problem to two
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Document Type: Book
All Authors / Contributors: Michael D Grigoriadis; Leonid Khachiyan
OCLC Number: 29419553
Notes: "May 1993."
Description: 17 leaves : illustrations ; 28 cm.
Series Title: Rutgers University.; Department of Computer Science.; Laboratory for Computer Science Research.; Technical report
Responsibility: M.D. Grigoriadis and L.G. Khachiyan.

Abstract:

Abstract: "An exponential potential-function reduction algorithm for convex block-angular optimization problems is described. These problems are characterized by K disjoint convex compact sets called blocks and M nonnegative-valued convex block-separable coupling inequalities with a nonempty interior. A given convex block-separable function is to be minimized. The method reduces the optimization problem to two resource- sharing problems. The first of these problems is solved to obtain a feasible solution interior to the coupling constraints. Starting from this solution, the algorithm proceeds to solve the second problem on the original constraints, but with a modified exponential potential function.

The method is shown to produce an [epsilon]-approximate solution in O(K(ln M)([epsilon]⁻² + ln K)) iterations, provided that there is a feasible solution sufficiently interior to the coupling inequalities. Each iteration consists of solving a subset of independent block problems, followed by a simple coordination step. Computational experiments with a set of large linear concurrent and minimum-cost multicommodity network flow problems suggest that the method can be practical for computing fast approximations to large instances."

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