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Investigating semi-infinite programs using penalty functions and Lagrangian methods

Published online by Cambridge University Press:  17 February 2009

Sven-Åke Gustafson
Sven-Åke Gustafson
Affiliation:
Department of Numerical Analysis and Computing Science, The Royal Institute of Technology, S-10044 Stockholm 70, Sweden.
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Abstract

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In this paper the relations between semi-infinite programs and optimisation problems with finitely many variables and constraints are reviewed. Two classes of convex semi-infinite programs are defined, one based on the fact that a convex set may be represented as the intersection of closed halfspaces, while the other class is defined using the representation of the elements of a convex set as convex combinations of points and directions. Extension to nonconvex problems is given. A common technique of solving a semi-infinite program computationally is to derive necessary conditions for optimality in the form of a nonlinear system of equations with finitely many equations and unknowns. In the three-phase algorithm, this system is constructed from the optimal solution of a discretised version of the given semi-infinite program. i.e. a problem with finitely many variables and constraints. The system is solved numerically, often by means of some linearisation method. One option is to use a direct analog of the familiar SOLVER method.

Type
Research Article
Information
The ANZIAM Journal , Volume 28 , Issue 2 , October 1986 , pp. 158 - 169
Copyright
Copyright © Australian Mathematical Society 1986

References

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