《《2016 A note on the use of vector barrier parameters for interior-point methods》.pdfVIP

European Journal of Operational Research 181 (2007) 571–585 /locate/ejor Continuous Optimization A note on the use of vector barrier parameters for interior-point methods Javier M. Moguerza a,*, Alberto Olivares a, Francisco J. Prieto b a School of Engineering, University Rey Juan Carlos, C/ Tulipan s/n, 28933 Mostoles, Madrid, Spain b Department of Statistics, University Carlos III, C/ Madrid 126, 28903 Getafe, Madrid, Spain Received 29 September 2004; accepted 1 August 2006 Available online 13 October 2006 Abstract A key feature to ensure desirable convergence properties in an interior-point method is the appropriate choice of an updating rule for the barrier parameter. In this work we analyze and describe updating rules based on the use of a vector of barrier parameters. We show that these updating rules are well defined and satisfy sufficient conditions to ensure con- vergence to the correct limit points. We also present some numerical results that illustrate the improved performance of these strategies compared to the use of a scalar barrier parameter. 2006 Elsevier B.V. All rights reserved. Keywords: Interior point methods; Primal-dual methods; Non-convex optimization; Central path 1. Introduction Interior-point methods can be used to compute local solutions for nonlinear, and possibly non-convex, problems of the form min f ðx Þ x s:t: cðx Þ ¼ 0; ð1Þ x P 0; n