On Long Step Path Following and SUMT for Linear and Quadratic Programming
We consider a long step barrier algorithm for the minimization of a convex quadratic objective subject to linear inequality constraints. The algorithm is a dual version of a method developed by Anstreicher et al. [Algorithmica, 10 (1993), pp. 365-382], and requires $O ( nL )$ or $O( \sqrt{n} L )$ it...
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| Published in: | SIAM journal on optimization Vol. 6; no. 1; pp. 33 - 46 |
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| Main Author: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
Philadelphia
Society for Industrial and Applied Mathematics
01.02.1996
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| Subjects: | |
| ISSN: | 1052-6234, 1095-7189 |
| Online Access: | Get full text |
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| Summary: | We consider a long step barrier algorithm for the minimization of a convex quadratic objective subject to linear inequality constraints. The algorithm is a dual version of a method developed by Anstreicher et al. [Algorithmica, 10 (1993), pp. 365-382], and requires $O ( nL )$ or $O( \sqrt{n} L )$ iterations to solve a problem with n constraints, depending on how the barrier parameter is reduced. As a corollary of our analysis we demonstrate that the classical SUMT algorithm, exactly as implemented in 1968, solves linear and quadratic programs in $O( \sqrt{n} L\log L )$ iterations, with proper initialization and choice of parameters. |
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| Bibliography: | ObjectType-Article-1 SourceType-Scholarly Journals-1 content type line 14 |
| ISSN: | 1052-6234 1095-7189 |
| DOI: | 10.1137/0806003 |