A primal-dual interior point method for nonlinear optimization over second-order cones

Authors:
Hiroshi Yamashita;Hiroshi Yabe
Affiliations:
Mathematical Systems Inc., Tokyo, Japan;Department of Mathematical Information Science, Faculty of Science, Tokyo University of Science, Tokyo, Japan
Venue:
Optimization Methods & Software
Year:
2009

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Abstract

In this paper, we are concerned with nonlinear minimization problems with second-order cone constraints. A primal-dual interior point method that uses a commutative class of search directions is considered. We propose a new primal-dual merit function by combining the barrier penalty function and the potential function within the framework of the line search strategy, and show the global convergence property of our method.