Abstract
| Original language | English |
|---|---|
| Pages (from-to) | 244-260 |
| Journal | SIAM Journal on Optimization |
| Volume | 22 |
| DOIs | |
| Publication status | Published - 2012 |
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Asequential parametric method for solving constrained minimization problems. / Beck, A.; Ben-Tal, A.; Tetruashvili, L.
In: SIAM Journal on Optimization, Vol. 22, 2012, p. 244-260.Research output: Contribution to journal › Article › Scientific › peer-review
TY - JOUR
T1 - Asequential parametric method for solving constrained minimization problems
AU - Beck, A.
AU - Ben-Tal, A.
AU - Tetruashvili, L.
PY - 2012
Y1 - 2012
N2 - In this paper, a method for solving constrained convex optimization problems is introduced. The problem is cast equivalently as a parametric unconstrained one, the (single) parameter being the optimal value of the original problem. At each stage of the algorithm the parameter is updated, and the resulting subproblem is only approximately solved. A linear rate of convergence of the parameter sequence is established. Using an optimal gradient method due to Nesterov [Dokl. Akad. Nauk SSSR, 269 (1983), pp. 543–547] to solve the arising subproblems, it is proved that the resulting gradient-based algorithm requires an overall of $O({\log(1/\varepsilon)}/ {\sqrt{\varepsilon}})$ inner iterations to obtain an $\varepsilon$-optimal and feasible solution. An image deblurring problem is solved, demonstrating the capability of the algorithm to solve large-scale problems within reasonable accuracy.
AB - In this paper, a method for solving constrained convex optimization problems is introduced. The problem is cast equivalently as a parametric unconstrained one, the (single) parameter being the optimal value of the original problem. At each stage of the algorithm the parameter is updated, and the resulting subproblem is only approximately solved. A linear rate of convergence of the parameter sequence is established. Using an optimal gradient method due to Nesterov [Dokl. Akad. Nauk SSSR, 269 (1983), pp. 543–547] to solve the arising subproblems, it is proved that the resulting gradient-based algorithm requires an overall of $O({\log(1/\varepsilon)}/ {\sqrt{\varepsilon}})$ inner iterations to obtain an $\varepsilon$-optimal and feasible solution. An image deblurring problem is solved, demonstrating the capability of the algorithm to solve large-scale problems within reasonable accuracy.
U2 - 10.1137/100800580
DO - 10.1137/100800580
M3 - Article
VL - 22
SP - 244
EP - 260
JO - SIAM Journal on Optimization
JF - SIAM Journal on Optimization
SN - 1052-6234
ER -