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Apex duality for constrained optimization

Published online by Cambridge University Press:  17 February 2009

R. J. Duffin ,
D. F. Karney  and
E. Z. Prisman
R. J. Duffin
Affiliation:
Department of Mathematics, Carnegie-Mellon University, Pittsburgh, PA 15213
D. F. Karney
Affiliation:
School of Business, Univeristy of Kansas, Lawrence, KS 66045
E. Z. Prisman
Affiliation:
College of Business Administration, Department of Finance, Arizona State University, Tempe, AZ 85287
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In this paper, we develop a duality theory for the Apex dual in the case of primal constraints. As suggested by Duffin in [4], the objective function in this framework is a weighted average of the Legendre-Lagrangian function evaluated at key points. We show that whenever this new dual is feasible there is no duality gap for this dual, and moreover, no duality gap for both the Lagrangian and Wolfe duals too. We conclude with an outline of an algorithm to solve constrained minimization problems in the Apex framework.

Type
Research Article
Information
The ANZIAM Journal , Volume 28 , Issue 1 , July 1986 , pp. 134 - 146
Copyright
Copyright © Australian Mathematical Society 1986

References

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