A smoothing Levenberg–Marquardt algorithm for semi-infinite programming

Ping Jin (), Chen Ling () and Huifei Shen ()

Computational Optimization and Applications, 2015, vol. 60, issue 3, 675-695

Abstract: In this paper, we present a smoothing Levenberg–Marquardt algorithm for the solution of the semi-infinite programming (SIP) problem. We first reformulate the KKT system of SIP problem into a system of constrained nonsmooth equations. Then we solve this system by a smoothing Levenberg–Marquardt algorithm. The feasibility is ensured via the aggregated constraint, and at each iteration of the presented algorithm only a quadratic programming has to be solved. Global and local superlinear convergence of this algorithm is established under a local error bound condition, which is much weaker than the nonsingularity condition. Preliminary numerical results are reported. Copyright Springer Science+Business Media New York 2015

Keywords: Semi-infinite programming (SIP) problem; KKT system; Nonsmooth equations; Smoothing Levenberg–Marquardt algorithm; Convergence; 49M15; 49M37; 65K15; 90C30; 90C46 (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10589-014-9698-0

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