Synopsis
1: Analysis over Cones.- 1.Convex cones.- 2.Recession cones.- 3.Cone closed sets.- 4.Cone monotonie functions.- 5.Cone continuous functions.- 6.Cone convex functions.- 7.Set-valued maps.- 2: Efficient Points and Vector Optimization Problems.- 1.Binary relations and partial orders.- 2.Efficient points.- 3.Existence of efficient points.- 4.Domination property.- 5.Vector optimization problems.- 3: Nonsmooth Vector Optimization Problems.- 1 .Contingent derivatives.- 2.Unconstrained problems.- 3.Constrained problems.- 4.Differentiable case.- 5.Convex case.- 4: Scalarization and Stability.- 1.Separation by monotonic functions.- 2.Scalar representations.- 3.Completeness of scalarization.- 4.Stability.- 5: Duality.- l.Lagrangean duality.- 2.Conjugate duality.- 3.Axiomatic duality.- 4.Duality and alternative.- 6: Structure of Optimal Solution Sets.- 1.General case.- 2.Linear case.- 3.Convex case.- 4.Quasiconvex case.- Comments.- References.
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