Semi-Infinite Programming pp 3-41 | Cite as

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

## 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.

## Keywords

Linear Inequality Geometric Programming Duality State Dual Program Subjective View## Preview

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