An Infeasible Interior-Point Algorithm for Stochastic Second-Order Cone Optimization
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Alzalg (J Optim Theory Appl 163(1):148–164, 2014) derived a homogeneous self-dual algorithm for stochastic second-order cone programs with finite event space. In this paper, we derive an infeasible interior-point algorithm for the same stochastic optimization problem by utilizing the work of Rangarajan (SIAM J Optim 16(4), 1211–1229, 2006) for deterministic symmetric cone programs. We show that the infeasible interior-point algorithm developed in this paper has complexity less than that of the homogeneous self-dual algorithm mentioned above. We implement the proposed algorithm to show that they are efficient.
KeywordsSecond-order cone programming Stochastic programming Infeasible interior-point algorithms Euclidean Jordan algebra
Mathematics Subject Classification90C25 90C06 90C15 90C30 90C51 90C60
A part of the first author’s work was performed while he was visiting The Center for Applied and Computational Mathematics at Rochester Institute of Technology, NY, USA. The work of the first author was supported in part by Deanship of Scientific Research at The University of Jordan. The authors thank the two expert anonymous referees for their valuable suggestions, whose constructive comments have greatly enhanced the paper.
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