SOS-Convex Semialgebraic Programs and its Applications to Robust Optimization: A Tractable Class of Nonsmooth Convex Optimization
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DOI: 10.1007/s11228-017-0456-1
Abstract: In this paper, we introduce a new class of nonsmooth convex functions called SOS-convex semialgebraic functions extending the recently proposed notion of SOS-convex polynomials. This class of nonsmooth convex functions covers many common nonsmooth functions… read more here.
Keywords: class nonsmooth; sos convex; convex; optimization ... See more keywords
Outer-approximation algorithms for nonsmooth convex MINLP problems
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DOI: 10.1080/02331934.2018.1434173
Abstract: Abstract In this work, we combine outer-approximation (OA) and bundle method algorithms for dealing with mixed-integer non-linear programming (MINLP) problems with nonsmooth convex objective and constraint functions. As the convergence analysis of OA methods relies… read more here.
Keywords: convex minlp; nonsmooth convex; outer approximation; minlp problems ... See more keywords
A quasi-Newton proximal bundle method using gradient sampling technique for minimizing nonsmooth convex functions
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DOI: 10.1080/10556788.2021.2023522
Abstract: This study aims to merge the well-established ideas of bundle and Gradient Sampling (GS) methods to develop an algorithm for locating a minimizer of a nonsmooth convex function. In the proposed method, with the help… read more here.
Keywords: nonsmooth convex; bundle methods; quasi newton; method ... See more keywords