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- Title
Interval Methods for Semi-Infinite Programs.
- Authors
Bhattacharjee, Binita; Green Jr., William H.; Barton, Paul I.
- Abstract
A new approach for the numerical solution of smooth, nonlinear semi-infinite programs whose feasible set contains a nonempty interior is presented. Interval analysis methods are used to construct finite nonlinear, or mixed-integer nonlinear, reformulations of the original semi-infinite program under relatively mild assumptions on the problem structure. En certain cases the finite reformulation is exact and can be solved directly for the global minimum of the semi-infinite program (SIP). In the general case. this reformulation is over-constrained relative to the SIP. such that solving it yields a guaranteed feasible upper bound to the SIP solution. This upper bound can then be refined using a subdivision procedure which is shown to converge to the true SIP solution with finite e-optimality. In particular. the method is shown to converge for SIPs which do not satisfy regularity assumptions required by reduction-based methods, and for which certain points in the feasible set are subject to an infinite number of active constraints. Numerical results are presented for a number of problems in the SIP literature. The solutions obtained are compared to those identified by reduction-based methods, the relative performances of the nonlinear and mixed-integer nonlinear formulations are studied, and the use of different inclusion functions in the finite reformulation is investigated.
- Subjects
MATHEMATICAL programming; ALGORITHMS; MATHEMATICS; INTERVAL analysis; NUMERICAL analysis; MATHEMATICAL optimization
- Publication
Computational Optimization & Applications, 2005, Vol 30, Issue 1, p63
- ISSN
0926-6003
- Publication type
Article
- DOI
10.1007/s10589-005-4556-8