期刊
SIAM JOURNAL ON OPTIMIZATION
卷 23, 期 1, 页码 353-380出版社
SIAM PUBLICATIONS
DOI: 10.1137/120864015
关键词
global optimization; pessimistic bilevel problem; computational complexity
资金
- Imperial College Junior Research Fellowship scheme, EPSRC [EP/C513584/1, EP/I014640/1]
- Leverhulme trust through the Philip Leverhulme Prize
We study a variant of the pessimistic bilevel optimization problem, which comprises constraints that must be satisfied for any optimal solution of a subordinate (lower-level) optimization problem. We present conditions that guarantee the existence of optimal solutions in such a problem, and we characterize the computational complexity of various subclasses of the problem. We then focus on problem instances that may lack convexity, but that satisfy a certain independence property. We develop convergent approximations for these instances, and we derive an iterative solution scheme that is reminiscent of the discretization techniques used in semi-infinite programming. We also present a computational study that illustrates the numerical behavior of our algorithm on standard benchmark instances.
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