Journal
JOURNAL OF GLOBAL OPTIMIZATION
Volume 44, Issue 2, Pages 235-250Publisher
SPRINGER
DOI: 10.1007/s10898-008-9321-y
Keywords
Generalized semi-infinite; Minimax; Bi-level; Globaloptimization; Min-max-min
Funding
- Engineering and Physical Sciences Research Council [EP/C519655/1, EP/C513584/1] Funding Source: researchfish
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We propose an algorithm for the global optimization of three problem classes: generalized semi-infinite, continuous coupled minimax and bi-level problems. We make no convexity assumptions. For each problem class, we construct an oracle that decides whether a given objective value is achievable or not. If a given value is achievable, the oracle returns a point with a value better than or equal to the target. A binary search is then performed until the global optimum is obtained with the desired accuracy. This is achieved by solving a series of appropriate finite minimax and min-max-min problems to global optimality. We use Laplace's smoothing technique and a simulated annealing approach for the solution of these problems. We present computational examples for all three problem classes.
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