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In this paper we give necessary and sufficient optimality conditions for a vector optimization problem over cones involving support functions in objective as well as constraints, using cone-convex and other related functions. We also associate a unified dual to the primal problem and establish weak, strong and converse duality results. A number of previously studied problems appear as special cases.
In this paper we establish necessary as well as
sufficient conditions for a given feasible point to be a global
minimizer of smooth minimization problems with mixed variables.
These problems, for instance, cover box constrained smooth minimization
problems and bivalent optimization problems. In particular, our
results provide necessary global optimality conditions for difference
convex minimization problems, whereas our sufficient conditions
give easily verifiable conditions for global optimality...
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