Abstract
We consider the following problem
, where a and b are analytic functions. The usual method for solving this type of problem can be viewed as based on the simplex method applied to the dual problem. In this paper a new primal method is presented.
First a characterisation of the extreme points of the feasible set (the basic solutions) is given. Then the pivot operation is described. If we define
, then constr(x) can be assumed to be finite if x is a basic solution. The pivot operation takes one of two forms: either one of the points in constr(x) is dropped and a new point introduced, or one of the points in constr(x) is perturbed to the left or right.
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References
Glashoff, K. and SA. Gustafson, “Linear optimization and approximation”, Springer-Verlag, New York, 1983.
Hettich, R., “A review of numerical methods for semi-infinite optimization”, in ‘Semi-infinite programming and applications’, ed. A. V. Fiacco and K. O. Kortanek, Springer-Verlag, Berlin, 1983.
Lewis, A.S., “Extreme points and purification algorithms in general linear programming”, this volume.
Nash, P., “Algebraic fundamentals of linear programming”, this volume.
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© 1985 Springer-Verlag Berlin Heidelberg
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Anderson, E.J. (1985). A New Primal Algorithm for Semi-Infinite Linear Programming. In: Anderson, E.J., Philpott, A.B. (eds) Infinite Programming. Lecture Notes in Economics and Mathematical Systems, vol 259. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46564-2_9
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DOI: https://doi.org/10.1007/978-3-642-46564-2_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-15996-4
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