Stochastic Separated Continuous Conic Programming: Strong Duality and a Solution Method
We study a new class of optimization problems called stochastic separated continuous conic programming (SSCCP). SSCCP is an extension to the optimization model called separated continuous conic programming (SCCP) which has applications in robust optimization and sign-constrained linear-quadratic con...
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| Veröffentlicht in: | Mathematical problems in engineering Jg. 2014; H. 1 |
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| Sprache: | Englisch |
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01.01.2014
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| Abstract | We study a new class of optimization problems called stochastic separated continuous conic programming (SSCCP). SSCCP is an extension to the optimization model called separated continuous conic programming (SCCP) which has applications in robust optimization and sign-constrained linear-quadratic control. Based on the relationship among SSCCP, its dual, and their discretization counterparts, we develop a strong duality theory for the SSCCP. We also suggest a polynomial-time approximation algorithm that solves the SSCCP to any predefined accuracy. |
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| AbstractList | We study a new class of optimization problems called stochastic separated continuous conic programming (SSCCP). SSCCP is an extension to the optimization model called separated continuous conic programming (SCCP) which has applications in robust optimization and sign-constrained linear-quadratic control. Based on the relationship among SSCCP, its dual, and their discretization counterparts, we develop a strong duality theory for the SSCCP. We also suggest a polynomial-time approximation algorithm that solves the SSCCP to any predefined accuracy. We study a new class of optimization problems called stochastic separated continuous conic programming (SSCCP). SSCCP is an extension to the optimization model called separated continuous conic programming (SCCP) which has applications in robust optimization and sign‐constrained linear‐quadratic control. Based on the relationship among SSCCP, its dual, and their discretization counterparts, we develop a strong duality theory for the SSCCP. We also suggest a polynomial‐time approximation algorithm that solves the SSCCP to any predefined accuracy. |
| Author | Wang, Xiaoqing |
| Author_xml | – sequence: 1 givenname: Xiaoqing surname: Wang fullname: Wang, Xiaoqing organization: Lingnan (University) College Sun Yat-sen University Guangzhou, Guangdong 510275 China sysu.edu.cn |
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| Copyright | Copyright © 2014 Xiaoqing Wang. Copyright © 2014 Xiaoqing Wang. Xiaoqing Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. |
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| DOI | 10.1155/2014/896591 |
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| References_xml | – volume: 7 start-page: 889 issue: 4 year: 1997 end-page: 912 ident: 16 article-title: A study of general dynamic network programs with arc time-delays – reference: Anderson E. J. A continuous model for job-shop scheduling [Ph.D. thesis] 1978 Cambridge, UK University of Cambridge – volume: 33 start-page: 1952 issue: 6 year: 1995 end-page: 1977 ident: 13 article-title: Forms of optimal solutions for separated continuous linear programs – volume: 452-453 start-page: 1127 year: 2012 end-page: 1132 ident: 25 article-title: An approximation algorithm for solving generalized separated continuous conic programming – volume: 11-12 start-page: 625 issue: 1–4 year: 1999 end-page: 653 ident: 27 article-title: Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones – volume: 10 start-page: 722 issue: 3 year: 2000 end-page: 731 ident: 17 article-title: Convergence of a general class of algorithms for separated continuous linear programs – reference: Bellman R. 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Linear Programming in Infinite-Dimensional Spaces: Theory and Applications 1987 Chichester, UK John Wiley & Sons MR893179 – volume: 197 start-page: 207 issue: 1 year: 1996 end-page: 226 ident: 15 article-title: Linear optimal control problems with piecewise analytic solutions – volume: 32 start-page: 1289 issue: 5 year: 1994 end-page: 1296 ident: 10 article-title: On the solutions of a class of continuous linear programs – volume: 30 start-page: 916 issue: 4 year: 2005 end-page: 938 ident: 21 article-title: Efficient algorithms for separated continuous linear programs: the multicommodity flow problem with holding costs and extensions – volume: 48 start-page: 2118 issue: 4 year: 2009 end-page: 2138 ident: 2 article-title: Separated continuous conic programming: strong duality and an approximation algorithm – volume: 37 start-page: 177 issue: 1 year: 1999 end-page: 210 ident: 19 article-title: A new algorithm for state-constrained separated continuous linear programs – reference: Wang X. 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| Snippet | We study a new class of optimization problems called stochastic separated continuous conic programming (SSCCP). SSCCP is an extension to the optimization model... We study a new class of optimization problems called stochastic separated continuous conic programming (SSCCP). SSCCP is an extension to the optimization model... |
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| SubjectTerms | Algorithms Approximation Conics Discretization Euclidean space Linear programming Mathematical analysis Mathematical models Mathematical problems Optimization Optimization models Polynomials Programming Random variables Robust control Stochasticity |
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| Title | Stochastic Separated Continuous Conic Programming: Strong Duality and a Solution Method |
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