Constrained Nonconvex Nonsmooth Optimization via Proximal Bundle Method

Yang Yang (), Liping Pang (), Xuefei Ma () and Jie Shen ()
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Yang Yang: Dalian University of Technology
Liping Pang: Dalian University of Technology
Xuefei Ma: Syracuse University
Jie Shen: Liaoning Normal University

Journal of Optimization Theory and Applications, 2014, vol. 163, issue 3, No 12, 900-925

Abstract: Abstract In this paper, we consider a constrained nonconvex nonsmooth optimization, in which both objective and constraint functions may not be convex or smooth. With the help of the penalty function, we transform the problem into an unconstrained one and design an algorithm in proximal bundle method in which local convexification of the penalty function is utilized to deal with it. We show that, if adding a special constraint qualification, the penalty function can be an exact one, and the sequence generated by our algorithm converges to the KKT points of the problem under a moderate assumption. Finally, some illustrative examples are given to show the good performance of our algorithm.

Keywords: Nonconvex optimization; Nonsmooth optimization; Constrained programming; Exact penalty functions; Proximal bundle methods; Lower- $$C^{2}$$ C 2; 90C26 (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (7)

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DOI: 10.1007/s10957-014-0523-9

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