Sequential Randomized Algorithms for Robust Convex Optimization

• 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
• DOI: 10.1109/TAC.2015.2423871

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.