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A programming problem with an Lp norm in the objective function

Published online by Cambridge University Press:  17 February 2009

Bertram Mond  and
Murray Schechter
Bertram Mond
Affiliation:
Department of Pure Mathematics, Latrobe University, Melbourne, Australia Department of Applied Mathematics, Technion, Israel Institute of Technology, Haifa, Israel.
Murray Schechter
Affiliation:
Department of Mathematics, Lehigh University, Bethlehem, Penna, U.S.A. Department of Applied Mathematics, Technion, Israel Institute of Technology, Haifa, Israel.
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Abstract

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We consider a programming problem in which the objective function is the sum of a differentiable function and the p norm of Sx, where S is a matrix and p > 1. The constraints are inequality constraints defined by differentiable functions. With the aid of a recent transposition theorem of Schechter we get a duality theorem and also a converse duality theorem for this problem. This result generalizes a result of Mond in which the objective function contains the square root of a positive semi-definite quadratic function.

Type
Research Article
Information
The ANZIAM Journal , Volume 19 , Issue 3 , June 1976 , pp. 333 - 342
Copyright
Copyright © Australian Mathematical Society 1976

References

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