A GENERALIZATION OF A THEOREM OF EDMUND EISENBERG
Systems research memo.
NORTHWESTERN UNIV EVANSTON IL TECHNOLOGICAL INST
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The convex duality theory as developed by Charnes -Cooper-Kortanek which is valid for non-differentiable quasi-concave functions is applied to derive a gradient inequality for a non-differentiable function involving a symmetric quadratic form with positivity required only on a given convex polyhedral cone, generalizing a theorem of Edmund Eisenberg. No assumption is needed either that the primal problem attain its extremal value, since the CCK duality theory includes this possibility. The theory directly applies to the non-homogeneous problem where now the given cone is replaced by the intersection of a finite number of half spaces.
- Operations Research