A smoothing Levenberg-Marquardt algorithm for semi-infinite programming

作者：Jin, Ping; Ling, Chen^*; Shen, Huifei

来源：Computational Optimization and Applications, 2015, 60(3): 675-695.

DOI：10.1007/s10589-014-9698-0

• Semi-infinite programming (SIP) problem
• KKT system
• Nonsmooth equations
• Smoothing Levenberg-Marquardt algorithm
• Convergence

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.

• 出版日期2015-4
• 单位杭州电子科技大学