An SQP method for minimization of locally Lipschitz functions with nonlinear constraints

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 an penalty function to equilibrate among the decrease of the objective function and the feasibility...

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Bibliographic Details
Published in:Optimization Vol. 68; no. 4; pp. 731 - 751
Main Authors: Yousefpour, Rohollah, Jafari, Elham
Format: Journal Article
Language:English
Published: Philadelphia Taylor & Francis 03.04.2019
Taylor & Francis LLC
Subjects:
Algorithms
Approximation
nonlinear constraint
Penalty function
Quadratic programming
Sequential quadratic model
ε-subdifferential
ISSN:0233-1934, 1029-4945
Online Access:Get full text
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Summary: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 an 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.
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ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2018.1545123