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Title: An interior-point ℓ 1/2-penalty method for inequality constrained nonlinear optimization
Authors: Tian, B
Yang, X 
Meng, K
Issue Date: Jul-2016
Source: Journal of industrial and management optimization, July 2016, v. 12, no. 3, p. 949-973
Abstract: In this paper, we study inequality constrained nonlinear programming problems by virtue of an ℓ1/2-penalty function and a quadratic relaxation. Combining with an interior-point method, we propose an interior-point ℓ 1/2-penalty method. We introduce different kinds of constraint qualifications to establish the first-order necessary conditions for the quadratically relaxed problem. We apply the modified Newton method to a sequence of logarithmic barrier problems, and design some reliable algorithms. Moreover, we establish the global convergence results of the proposed method. We carry out numerical experiments on 266 inequality constrained optimization problems. Our numerical results show that the proposed method is competitive with some existing interior-point ℓ1-penalty methods in term of iteration numbers and better when comparing the values of the penalty parameter.
Keywords: Constraint qualification
Lower-order penalty function
Nonlinear programming
Primal-dual interior-point method
Quadratic relaxation
Publisher: American Institute of Mathematical Sciences
Journal: Journal of industrial and management optimization 
ISSN: 1547-5816
EISSN: 1553-166X
DOI: 10.3934/jimo.2016.12.949
Rights: This article has been published in a revised form in Journal of Industrial and Management Optimization This version is free to download for private research and study only. Not for redistribution, re-sale or use in derivative works.
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