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 Rangar...
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| Published in | Journal of optimization theory and applications Vol. 181; no. 1; pp. 324 - 346 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
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Springer US
01.04.2019
Springer Nature B.V |
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| Online Access | Get full text |
| ISSN | 0022-3239 1573-2878 |
| DOI | 10.1007/s10957-018-1445-8 |
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| Abstract | 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. |
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| AbstractList | 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. 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. |
| Author | Alzalg, Baha Badarneh, Khaled Ababneh, Ayat |
| Author_xml | – sequence: 1 givenname: Baha surname: Alzalg fullname: Alzalg, Baha email: b.alzalg@ju.edu.jo organization: Department of Mathematics, The University of Jordan, School of Mathematical Sciences, Rochester Institute of Technology – sequence: 2 givenname: Khaled surname: Badarneh fullname: Badarneh, Khaled organization: Department of Mathematics, The University of Jordan – sequence: 3 givenname: Ayat surname: Ababneh fullname: Ababneh, Ayat organization: Department of Mathematics, The University of Jordan, Department of Mathematics, The Ohio State University |
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| Cites_doi | 10.1137/S1052623494269035 10.1137/S1052623495290209 10.1080/10556789808805691 10.1016/S0252-9602(08)60058-2 10.1007/s10589-006-9000-1 10.1007/s10107-002-0339-5 10.1137/S1052623495294955 10.1016/j.apm.2011.12.053 10.1007/s10107-010-0341-2 10.1137/S1052623495296115 10.1007/s10957-013-0428-z 10.1137/0806020 10.1016/j.jmaa.2013.07.075 10.1137/040606557 10.1137/S1052623495293056 10.1007/s10107-003-0380-z 10.1016/j.amc.2014.10.015 10.1016/j.amc.2015.05.014 |
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| Keywords | 90C51 90C30 Euclidean Jordan algebra 90C25 90C06 90C15 Infeasible interior-point algorithms 90C60 Second-order cone programming Stochastic programming |
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| References | Alizadeh, Goldfarb (CR2) 2003; 95 Rangarajan (CR8) 2006; 16 Schmieta, Alizadeh (CR15) 2003; 96 Alzalg (CR1) 2012; 36 Alzalg (CR4) 2014; 249 Potra, Sheng (CR9) 1998; 8 CR7 Helmberg, Rendl, Vanderbei, Wolkowicz (CR16) 1996; 6 Potra, Sheng (CR19) 1998; 9 Alzalg, Ariyawansa (CR3) 2014; 409 Xiaoni, Sanyang (CR10) 2008; 28 Alzalg (CR6) 2014; 163 Alzalg (CR5) 2015; 256 Castro, Cuesta (CR12) 2011; 130 Alzalg, Maggiono, Vitali (CR20) 2016; 99 Nesterov, Todd (CR18) 1998; 8 De Klerk, Roos, Terlaky (CR21) 1998; 18 Monteiro (CR13) 1997; 7 Zhang (CR14) 1998; 8 Castro (CR11) 2007; 36 Kojima, Shindoh, Hara (CR17) 1997; 7 B Alzalg (1445_CR3) 2014; 409 F Alizadeh (1445_CR2) 2003; 95 J Castro (1445_CR11) 2007; 36 Y Zhang (1445_CR14) 1998; 8 YE Nesterov (1445_CR18) 1998; 8 B Alzalg (1445_CR1) 2012; 36 M Kojima (1445_CR17) 1997; 7 F Potra (1445_CR9) 1998; 8 B Alzalg (1445_CR20) 2016; 99 E Klerk De (1445_CR21) 1998; 18 J Castro (1445_CR12) 2011; 130 B Alzalg (1445_CR4) 2014; 249 B Alzalg (1445_CR5) 2015; 256 B Alzalg (1445_CR6) 2014; 163 BK Rangarajan (1445_CR8) 2006; 16 F Potra (1445_CR19) 1998; 9 SH Schmieta (1445_CR15) 2003; 96 C Xiaoni (1445_CR10) 2008; 28 C Helmberg (1445_CR16) 1996; 6 RD Monteiro (1445_CR13) 1997; 7 1445_CR7 |
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2014
) derived a homogeneous self-dual algorithm for stochastic second-order cone programs with finite event space.... 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.... |
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| SubjectTerms | Algorithms Applications of Mathematics Calculus of Variations and Optimal Control; Optimization Engineering Mathematics Mathematics and Statistics Operations Research/Decision Theory Optimization Theory of Computation |
| Title | An Infeasible Interior-Point Algorithm for Stochastic Second-Order Cone Optimization |
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