期刊
OPTIMIZATION METHODS & SOFTWARE
卷 24, 期 3, 页码 381-406出版社
TAYLOR & FRANCIS LTD
DOI: 10.1080/10556780802712889
关键词
robust optimization; cutting-set methods; semi-infinite programming; minimax optimization; games
类别
资金
- Dr Dennis Healy of DARPAMTO [N00014-05-1-0700]
- Office of Naval Research
- NSF [0529426]
- AFOSR [FA9550-06-1-0312]
We consider a general worst-case robust convex optimization problem, with arbitrary dependence on the uncertain parameters, which are assumed to lie in some given set of possible values. We describe a general method for solving such a problem, which alternates between optimization and worst-case analysis. With exact worst-case analysis, the method is shown to converge to a robust optimal point. With approximate worst-case analysis, which is the best we can do in many practical cases, the method seems to work very well in practice, subject to the errors in our worst-case analysis. We give variations on the basic method that can give enhanced convergence, reduce data storage, or improve other algorithm properties. Numerical simulations suggest that the method finds a quite robust solution within a few tens of steps; using warm-start techniques in the optimization steps reduces the overall effort to a modest multiple of solving a nominal problem, ignoring the parameter variation. The method is illustrated with several application examples.
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