Acceleration techniques for level bundle methods in weakly smooth convex constrained optimization

Yunmei Chen (), Xiaojing Ye () and Wei Zhang ()
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Yunmei Chen: University of Florida
Xiaojing Ye: George State University
Wei Zhang: University of Florida

Computational Optimization and Applications, 2020, vol. 77, issue 2, No 4, 432 pages

Abstract: Abstract 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.

Keywords: Convex optimization; Acceleration; Bundle method; Functional constrained optimization (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10589-020-00208-9

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