Primal-dual interior-point algorithms for convex quadratic circular cone optimization

Yanqin  Bai; Xuerui  Gao; Guoqiang  Wang

doi:10.3934/naco.2015.5.211

Article Contents

2015, Volume 5, Issue 2: 211-231. Doi: 10.3934/naco.2015.5.211

This issue Previous Article Continuity and stability of two-stage stochastic programs with quadratic continuous recourse Next Article

Primal-dual interior-point algorithms for convex quadratic circular cone optimization

1.
Department of Mathematics, Shanghai University, Shanghai 200444
2.
College of Fundamental Studies, Shanghai University of Engineering Science, Shanghai 201620

Received: November 30, 2014

Revised: April 30, 2015

Published: May 2015

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Abstract

In this paper we focus on a class of special nonsymmetric cone optimization problem called circular cone optimization problem, which has a convex quadratic function as the objective function and an intersection of a non-self-dual circular cone and linear equations as the constraint condition. Firstly we establish the algebraic relationships between the circular cone and the second-order cone and translate the original problem from the circular cone optimization problem to the second-order cone optimization problem. Then we present kernel-function based primal-dual interior-point algorithms for solving this special circular cone optimization and derive the iteration bounds for large- and small-update methods. Finally, some preliminary numerical results are provided to demonstrate the computational performance of the proposed algorithms.

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Mathematics Subject Classification: Primary: 90C05, 90C51; Secondary: 65K05.

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