Acceleration techniques for level bundle methods in weakly smooth convex constrained optimization
| Autor: | Yunmei Chen, Xiaojing Ye, Wei Zhang |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Mathematical optimization
021103 operations research Control and Optimization Applied Mathematics 0211 other engineering and technologies Constrained optimization Regular polygon Acceleration (differential geometry) 010103 numerical & computational mathematics 02 engineering and technology Bundle methods 01 natural sciences Computational Mathematics Component (UML) Convex optimization Constraint functions 0101 mathematics Mathematics |
| Zdroj: | Computational Optimization and Applications. 77:411-432 |
| ISSN: | 1573-2894 0926-6003 |
| DOI: | 10.1007/s10589-020-00208-9 |
| Popis: | We develop a unified level-bundle method, called accelerated constrained level-bundle (ACLB) algorithm, for solving constrained convex optimization problems. where the objective and constraint functions can be nonsmooth, weakly smooth, and/or smooth. ACLB employs Nesterov’s accelerated gradient technique, and hence retains the iteration complexity as that of existing bundle-type methods if the objective or one of the constraint functions is nonsmooth. More importantly, ACLB can significantly reduce iteration complexity when the objective and all constraints are (weakly) smooth. In addition, if the objective contains a nonsmooth component which can be written as a specific form of maximum, we show that the iteration complexity of this component can be much lower than that for general nonsmooth objective function. Numerical results demonstrate the effectiveness of the proposed algorithm. |
| Databáze: | OpenAIRE |
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