Sequential Randomized Algorithms for Robust Convex Optimization
Sequential randomized algorithms are considered for robust convex optimization which minimizes a linear objective function subject to a parameter dependent convex constraint. Employing convex optimization and random sampling of parameter, these algorithms enable us to obtain a suboptimal solution wi...
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| Vydáno v: | IEEE transactions on automatic control Ročník 60; číslo 12; s. 3356 - 3361 |
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| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
New York
IEEE
01.12.2015
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Témata: | |
| ISSN: | 0018-9286, 1558-2523 |
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| Abstract | Sequential randomized algorithms are considered for robust convex optimization which minimizes a linear objective function subject to a parameter dependent convex constraint. Employing convex optimization and random sampling of parameter, these algorithms enable us to obtain a suboptimal solution within reasonable computational time. The suboptimal solution is feasible in a probabilistic sense and the suboptimal value belongs to an interval which contains the optimal value. The maximum of the interval is the optimal value of the robust convex optimization plus a specified tolerance. On the other hand, its minimum is the optimal value of the chance constrained optimization which is a probabilistic relaxation of the robust convex optimization, with high probability. |
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| AbstractList | Sequential randomized algorithms are considered for robust convex optimization which minimizes a linear objective function subject to a parameter dependent convex constraint. Employing convex optimization and random sampling of parameter, these algorithms enable us to obtain a suboptimal solution within reasonable computational time. The suboptimal solution is feasible in a probabilistic sense and the suboptimal value belongs to an interval which contains the optimal value. The maximum of the interval is the optimal value of the robust convex optimization plus a specified tolerance. On the other hand, its minimum is the optimal value of the chance constrained optimization which is a probabilistic relaxation of the robust convex optimization, with high probability. |
| Author | Fujisaki, Yasumasa Wada, Takayuki |
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| Keywords | Optimization algorithms robust control randomized algorithms |
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| References | ref13 tempo (ref4) 2013 ref12 ref15 ref14 ben-tal (ref1) 2009 ref11 ref22 ref10 ref21 ref2 ref16 tarasov (ref17) 1988; 37 ref19 ref18 ref8 ref7 ref9 ref3 ref6 ref5 goffin (ref20) 1999; 84 |
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| SubjectTerms | Convex functions Ellipsoids Linear programming Optimization Optimization algorithms Probabilistic logic Randomized algorithms Robust control Robustness Upper bound |
| Title | Sequential Randomized Algorithms for Robust Convex Optimization |
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