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A duality theorem for nondifferentiable convex programming with operatorial constraints

Published online by Cambridge University Press:  17 April 2009

P. Kanniappan  and
Sundaram M.A. Sastry
P. Kanniappan
Affiliation:
Department of Mathematics, Gandhigram Rural Institute, Gandhigram, India
Sundaram M.A. Sastry
Affiliation:
School of Mathematics, Madurai Kamaraj University, Madurai - 21, India.
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Abstract

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A duality theorem of Wolfe for non-linear differentiable programming is now extended to minimization of a non-differentiable, convex, objective function defined on a general locally convex topological linear space with a non-differentiable operatorial constraint, which is regularly subdifferentiable. The gradients are replaced by subgradients. This extended duality theorem is then applied to a programming problem where the objective function is the sum of a positively homogeneous, lower semi continuous, convex function and a subdifferentiable, convex function. We obtain another duality theorem which generalizes a result of Schechter.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 22 , Issue 1 , August 1980 , pp. 145 - 152
Copyright
Copyright © Australian Mathematical Society 1980

References

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