Linear programming with nonparametric penalty programs and iterated thresholding
It is known [Mangasarian, A Newton method for linear programming, J. Optim. Theory Appl. 121 (2004), pp. 1-18] that every linear program can be solved exactly by minimizing an unconstrained quadratic penalty program. The penalty program is parameterized by a scalar t>0, and one is able to solve...
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| Vydáno v: | Optimization methods & software Ročník 38; číslo 1; s. 107 - 127 |
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| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Abingdon
Taylor & Francis
02.01.2023
Taylor & Francis Ltd |
| Témata: | |
| ISSN: | 1055-6788, 1029-4937 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | It is known [Mangasarian, A Newton method for linear programming, J. Optim. Theory Appl. 121 (2004), pp. 1-18] that every linear program can be solved exactly by minimizing an unconstrained quadratic penalty program. The penalty program is parameterized by a scalar t>0, and one is able to solve the original linear program in this manner when t is selected larger than a finite, but unknown
. In this paper, we show that every linear program can be solved using the solution to a parameter-free penalty program. We also characterize the solutions to the quadratic penalty programs using fixed points of certain nonexpansive maps. This leads to an iterative thresholding algorithm that converges to a desired limit point. We show in numerical experiments that this iterative method can outperform a variety of standard quadratic program solvers. Finally, we show that for every
, the solution one obtains by solving a parameterized penalty program is guaranteed to lie in the feasible set of the original linear program. |
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| Bibliografie: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ISSN: | 1055-6788 1029-4937 |
| DOI: | 10.1080/10556788.2022.2117356 |