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On the 1962–1972 Decade of Semi-Infinite Programming: A Subjective View

  • Chapter
Semi-Infinite Programming

Part of the book series: Nonconvex Optimization and Its Applications ((NOIA,volume 57))

Abstract

Several major themes developed during this, the apparent first of almost four decades of semi-infinite programming, are reviewed in this paper.

One theme was the development of a dual program to the problem of minimizing an arbitrary convex function over an arbitrary convex set in the n-space that featured the maximization of a linear functional in non-negative variables of a generalized finite sequence space subject to a finite system of linear inequalities. A characteristic of the dual program was that it did not involve any primal variables occurring within an internal optimization.

A second major theme was the introduction of an “infinity” into systems of semi-infinite linear inequalities, a manifestation of the “probing” between analysis and algebra.

In finite linear programming there are four mutually exclusive and collectively exhaustive duality states that can occur, and this led to the third theme of developing a classification theory for linear semi-infinite programming that included finite linear programming as a special case.

The fourth theme was one of algorithmic development. Finally, throughout the decade there was an emphasis on applications, principally to Economics, Game Theory, Asymptotic Lagrange Regularity, Air Pollution Abatement, and Geometric Programming.

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  1. Department of Management Sciences, Tippie College of Business and the Program in Applied Mathematical & Computational Sciences, University of Iowa, Iowa City, IA, 52242, USA

    Ken O. Kortanek

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  1. Universidad de Alicante, Spain

    Miguel Á. Goberna  & Marco A. López  & 

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Kortanek, K.O. (2001). On the 1962–1972 Decade of Semi-Infinite Programming: A Subjective View. In: Goberna, M.Á., López, M.A. (eds) Semi-Infinite Programming. Nonconvex Optimization and Its Applications, vol 57. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3403-4_1

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