An SQP method for minimization of locally Lipschitz functions with nonlinear constraints. (3rd April 2019)

• Record Type: Journal Article
• Authors: Yousefpour, Rohollah; Jafari, Elham
• Is Part Of: Optimization. Volume 68:Number 4(2019)
• Page Start: 731
• Page End: 751
• Publication Date: 2019-04-03
• Subjects: Sequential quadratic model -- l1 penalty function -- ε-subdifferential -- nonlinear constraint; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2018.1545123
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract: In this paper, we present a quadratic model for minimizing problems with nonconvex and nonsmooth objective and constraint functions. This method is based on sequential quadratic programming that uses anl 1 penalty function to equilibrate among the decrease of the objective function and the feasibility of the constraints. To construct a quadratic subproblem, we linearize the objective and constraint functions with their ε -subdifferential approximations. These approximations are iteratively improved until an effective descent direction is found. Also, we prove that our method is globally convergent in the sense that, every accumulation point of the generated sequence is a Clark-stationary point for the penalty function. Finally, the presented algorithm is implemented in Matlab environment and compared with some recent methods.