An Infeasible Interior-Point Algorithm for Stochastic Second-Order Cone Optimization

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.

[1]  Florian A. Potra,et al.  A Superlinearly Convergent Primal-Dual Infeasible-Interior-Point Algorithm for Semidefinite Programming , 1998, SIAM J. Optim..

[2]  Baha Alzalg.  Volumetric barrier decomposition algorithms for stochastic quadratic second-order cone programming , 2015, Appl. Math. Comput..

[3]  Renato D. C. Monteiro,et al.  Primal-Dual Path-Following Algorithms for Semidefinite Programming , 1997, SIAM J. Optim..

[4]  Farid Alizadeh,et al.  Extension of primal-dual interior point algorithms to symmetric cones , 2003, Math. Program..

[5]  K. A. Ariyawansa,et al.  Logarithmic barrier decomposition-based interior point methods for stochastic symmetric programming , 2014 .

[6]  Liu San-yang,et al.  An infeasible-interior-point predictor-corrector algorithm for the second-order cone program , 2008 .

[7]  Shinji Hara,et al.  Interior-Point Methods for the Monotone Semidefinite Linear Complementarity Problem in Symmetric Matrices , 1997, SIAM J. Optim..

[8]  Jordi Castro,et al.  Quadratic regularizations in an interior-point method for primal block-angular problems , 2011, Math. Program..

[9]  Baha Alzalg.  Homogeneous Self-dual Algorithms for Stochastic Second-Order Cone Programming , 2014, J. Optim. Theory Appl..

[10]  Baha Alzalg.  Decomposition-based interior point methods for stochastic quadratic second-order cone programming , 2014, Appl. Math. Comput..

[11]  Bharath Kumar Rangarajan,et al.  Polynomial Convergence of Infeasible-Interior-Point Methods over Symmetric Cones , 2006, SIAM J. Optim..

[12]  Jordi Castro,et al.  An interior-point approach for primal block-angular problems , 2007, Comput. Optim. Appl..

[13]  Baha Alzalg,et al.  Stochastic second-order cone programming: Applications models , 2012 .

[14]  Yin Zhang,et al.  On Extending Some Primal-Dual Interior-Point Algorithms From Linear Programming to Semidefinite Programming , 1998, SIAM J. Optim..

[15]  F. Potra,et al.  On homogeneous interrior-point algorithms for semidefinite programming , 1998 .

[16]  Baha Alzalg,et al.  HOMOGENEOUS SELF-DUAL METHODS FOR SYMMETRIC CONES UNDER UNCERTAINTY , 2016 .

[17]  Michael J. Todd,et al.  Primal-Dual Interior-Point Methods for Self-Scaled Cones , 1998, SIAM J. Optim..

[18]  Donald Goldfarb,et al.  Second-order cone programming , 2003, Math. Program..

[19]  Robert J. Vanderbei,et al.  An Interior-Point Method for Semidefinite Programming , 1996, SIAM J. Optim..