A note on semi-infinite program bounding methods

被引:0
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作者
Stuart M. Harwood
Dimitri J. Papageorgiou
Francisco Trespalacios
机构
[1] ExxonMobil Research and Engineering Company,Corporate Strategic Research
来源
Optimization Letters | 2021年 / 15卷
关键词
Semi-infinite programming; Global optimization; Lower bounds;
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摘要
Semi-infinite programs are a class of mathematical optimization problems with a finite number of decision variables and infinite constraints. As shown by Blankenship and Falk (J Optim Theory Appl 19(2):261–281, 1976), a sequence of lower bounds which converges to the optimal objective value may be obtained with specially constructed finite approximations of the constraint set. In Mitsos (Optimization 60(10–11):1291–1308, 2011), it is claimed that a modification of this lower bounding method involving approximate solution of the lower-level program yields convergent lower bounds. We show with a counterexample that this claim is false, and discuss what kind of approximate solution of the lower-level program is sufficient for correct behavior.
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页码:1485 / 1490
页数:5
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