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.
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Ferris, M.C., Philpott, A.B. An interior point algorithm for semi-infinite linear programming. Mathematical Programming 43, 257–276 (1989). https://doi.org/10.1007/BF01582293
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DOI: https://doi.org/10.1007/BF01582293