# Optimization problems; Introduction

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## Abstract

If a problem in the real world is described (and thus necessarily idealized) by a mathematical model, then the problem often calls for maximizing, or minimizing, some function of the variables which describe the problem. For example, it may be required to calculate the conditions of operation of an industrial process which give the maximum output, or quality, or which give the minimum cost. Such calculations differ from the classical ‘maximum-minimum’ problems of the calculus textbooks, because the variables of the problem are nearly always subject to restrictions — equations or inequalities — called *constraints*. It is therefore not enough to equate a derivative, or gradient, to zero to find a maximum or minimum.

## Keywords

Banach Space Optimal Control Problem Mathematical Program Convex Cone Piecewise Continuous Function## Preview

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## References

- Craven, B.D., and Mond, B. (1973), Transposition theorems for cone-convex functions,
*SIAM J. Appl. Math.*,**24**, 603–612.CrossRefGoogle Scholar - Dieudonné, J. (1960),
*Foundations of Modern Analysis*, Academic Press, New York.Google Scholar - Gray, P., and Cullinan-Jones, C. (1976), Applied Optimization — a Survey,
*Interfaces*,**6**(3), 24–46.CrossRefGoogle Scholar - Simmons, G.F. (1963),
*Introduction to Topology and Modern Anal Analysis*, McGraw-Hill/Kogakusha, Tokyo.Google Scholar