Abstract
Many design objectives may be formulated as semi-infinite constraints. Examples in control design, for example, include hard constraints on time and frequency responses and robustness constraints. A useful algorithm for solving such inequalities is the outer approximations algorithm. One version of an outer approximations algorithm for solving an infinite set of inequalitiesϕ(x, y) ≤0 for allyεY proceeds by solving, at iterationi of the master algorithm, a finite set of inequalities (ϕ(x, y) ≤0 for allyεY i) to yieldx i and then updatingY i toY i+1=Y i ∪ {yi } wherey iε arg max {ϕ(x i,y)¦yε Y}. Since global optimization is computationally extremely expensive, it is desirable to reduce the number of such optimizations. We present, in this paper, a modified version of the outer approximations algorithm which achieves this objective.
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Communicated by S. K. Mitter
The research reported herein was sponsored by the National Science Foundation Grants ECS-9024944, ECS-8816168, the Air Force Office of Scientific Research Contract AFOSR-90-0068, and the NSERC of Canada under Grant OGPO-138352.
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Mayne, D.Q., Michalska, H. & Polak, E. An efficient algorithm for solving semi-infinite inequality problems with box constraints. Appl Math Optim 30, 135–157 (1994). https://doi.org/10.1007/BF01189451
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DOI: https://doi.org/10.1007/BF01189451