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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Bibliographic Details
Published in:IEEE transactions on automatic control Vol. 60; no. 12; pp. 3356 - 3361
Main Authors: Wada, Takayuki, Fujisaki, Yasumasa
Format: Journal Article
Language:English
Published: New York IEEE 01.12.2015
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Convex functions
Ellipsoids
Linear programming
Optimization
Optimization algorithms
Probabilistic logic
Randomized algorithms
Robust control
Robustness
Upper bound
Optimization algorithms
robust control
randomized algorithms
ISSN:0018-9286, 1558-2523
Online Access:Get full text
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Summary: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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ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2015.2423871