Open AccessAn interior-point $l_{\frac{1}{2}}$-penalty method for inequality constrained nonlinear optimization
Author(s) -
Boshi Tian,
Xiaoqi Yang,
Kaiwen Meng
Publication year - 2015
Publication title -
journal of industrial and management optimization
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.325
H-Index - 32
eISSN - 1553-166X
pISSN - 1547-5816
DOI - 10.3934/jimo.2016.12.949
Subject(s) - penalty method , interior point method , mathematics , nonlinear programming , mathematical optimization , constraint (computer aided design) , relaxation (psychology) , constrained optimization , logarithm , sequential quadratic programming , convergence (economics) , quadratic equation , nonlinear system , quadratic growth , point (geometry) , function (biology) , sequence (biology) , quadratic programming , mathematical analysis , psychology , social psychology , physics , geometry , quantum mechanics , economics , economic growth , genetics , evolutionary biology , biology
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.Department of Applied Mathematic