On the Resolution of Linearly Constrained Convex Minimization Problems
The problem of minimizing a twice differentiable convex function $f$ is considered, subject to $Ax = b, x \geq 0$, where $A \in \mathbb{R}^{M \times N} ,M,N$ are large and the feasible region is bounded. It is proven that this problem is equivalent to a "primal-dual" box-constrained proble...
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| Published in | SIAM journal on optimization Vol. 4; no. 2; pp. 331 - 339 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Philadelphia
Society for Industrial and Applied Mathematics
01.05.1994
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| Subjects | |
| Online Access | Get full text |
| ISSN | 1052-6234 1095-7189 |
| DOI | 10.1137/0804018 |
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| Abstract | The problem of minimizing a twice differentiable convex function $f$ is considered, subject to $Ax = b, x \geq 0$, where $A \in \mathbb{R}^{M \times N} ,M,N$ are large and the feasible region is bounded. It is proven that this problem is equivalent to a "primal-dual" box-constrained problem with $2N + M$ variables. The equivalent problem involves neither penalization parameters nor ad hoc multiplier estimators. This problem is solved using an algorithm for bound constrained minimization that can deal with many variables. Numerical experiments are presented. |
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| AbstractList | The problem of minimizing a twice differentiable convex function $f$ is considered, subject to $Ax = b, x \geq 0$, where $A \in \mathbb{R}^{M \times N} ,M,N$ are large and the feasible region is bounded. It is proven that this problem is equivalent to a "primal-dual" box-constrained problem with $2N + M$ variables. The equivalent problem involves neither penalization parameters nor ad hoc multiplier estimators. This problem is solved using an algorithm for bound constrained minimization that can deal with many variables. Numerical experiments are presented. |
| Author | Martínez, José Mario Santos, Sandra A. Friedlander, Ana |
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| Cites_doi | 10.1007/BF01396045 10.1137/0728030 10.1090/S0025-5718-1988-0929544-3 10.1109/42.52985 10.1109/42.61759 10.1111/j.2517-6161.1990.tb01798.x 10.1137/0804010 10.1137/0801008 10.1007/BF00940348 10.1137/0725029 |
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| References | R2 R4 Green P. (R8) 1990; 52 Yabe Hiroshi (R16) 1991; 27 R9 Dembo Ron S. (R5) 1985 R10 R11 Duff I. S. (R6) 1986 R14 R13 R15 Fletcher R. (R7) 1987 R1 |
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| Title | On the Resolution of Linearly Constrained Convex Minimization Problems |
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