Necessary and sufficient conditions in constrained optimization

Additional conditions are attached to the Kuhn-Tucker conditions giving a set of conditions which are both necessary and sufficient for optimality in constrained optimization, under appropriate constraint qualifications. Necessary and sufficient conditions are also given for optimality of the dual problem. Duality and converse duality are treated accordingly.     

Cohomology of the complement of a free divisor

We prove that if is a ``strongly quasihomogeneous" free divisor in the Stein manifold , and is its complement, then the de Rham cohomology of can be computed as the cohomology of the complex of meromorphic differential forms on with logarithmic poles along , with exterior derivative. The class of strongly quasihomogeneous free divisors, introduced here, includes free hyperplane arrangements and the discriminants of stable mappings in Mather's nice dimensions (and in particular the discriminants of Coxeter groups).

     

Thermal stability of products prepared by the combination of cyclodextrins and zeolites

Derivatographic and calorimetric measurements were used to study the thermal properties of combined inclusion compounds of zeolite-cyclodextrin type and of zeolite-cyclodextrin-pharmaceutical type. There were differences in the characteristic decomposition temperature intervals and in the modes of cyclodextrin and pharmaceutical liberation from the products. Calorimetric measurements revealed that the process in the newly-formed complex host is connected with a glass transition. The products are intended for use in veterinary medicine.     

Complex nonlinear programming: Duality with invexity and equivalent real programs

Necessary conditions for optimality in polyhedral-cone constrained nonlinear complex programs are shown to be sufficient under the assumption of a particular form of invexity. Duality results are thus extended for a Wolfe-type dual. The formulation of real programs equivalent to complex programs via generating matrices is presented.     

Complementarity for arbitrary cones

Summary A complementarity theorem ofDantzig andCottle, for inequality-constrained minimization problems, is generalized both to inequalities involving arbitrary cones, and to problems in complex spaces. Various known theorems on duality and converse duality then follow, for both real and complex spaces.

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Zusammenfassung Ein Theorem vonDantzig undCottle für Minimumprobleme, deren Restriktionen durch Ungleichungen gegeben sind, wird in zwei Richtungen verallgemeinert: Auf Kegel als zulässige Mengen sowie auf Probleme im Komplexen. Daraus folgen verschiedene bekannte Dualitätsaussagen für reelle und komplexe Räume.

     

Symmetric dual fractional programming

A pair of symmetric dual fractional programming problems is formulated and appropriate duality theorems are established.

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Zusammenfassung Es wird ein symmetrisches Paar primaler und dualer Quotientenprogramme eingeführt, für das Dualitätsbeziehungen hergeleitet werden.

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Research by this author was carried out while he was a visiting research fellow at the University of Melbourne.     

On sufficient optimality conditions for mathematical programs with equaiity constraints

A number of sufficiency theorems in the mathematical programming literature, concerning problems with equality constraints, are shown to be trivial consequences of the corresponding results for inequality constraints.This work was supported by NSF Grant No. ECS-8214081. Research by the first author was done while a visitor at La Trobe University.