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An interior point algorithm for semi-infinite linear programming |
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| Authors: | M. C. Ferris A. B. Philpott |
| Affiliation: | (1) Cambridge University Engineering Department, Cambridge, England;(2) Present address: Department of Computer Sciences, University of Wisconsin, Madison, WI, USA;(3) Present address: Department of Theoretical and Applied Mechanics, University of Auckland, Auckland, New Zealand |
| Abstract: | We consider the generalization of a variant of Karmarkar's algorithm to semi-infinite programming. The extension of interior point methods to infinite-dimensional linear programming is discussed and an algorithm is derived. An implementation of the algorithm for a class of semi-infinite linear programs is described and the results of a number of test problems are given. We pay particular attention to the problem of Chebyshev approximation. Some further results are given for an implementation of the algorithm applied to a discretization of the semi-infinite linear program, and a convergence proof is given in this case. |
| Keywords: | Semi-infinite linear programming discretizations Karmarkar's method Chebyshev approximation |
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