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http://hdl.handle.net/10397/43771
| 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 http://dx.doi.org/10.3934/jimo.2016.12.949. This version is free to download for private research and study only. Not for redistribution, re-sale or use in derivative works. |
| Appears in Collections: | Journal/Magazine Article |
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|---|---|---|---|---|
| Yang_Interior-Point_Method_Inequality.pdf | Pre-Published version | 433.85 kB | Adobe PDF | View/Open |
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