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Weak minimization and duality |
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| Authors: | T Weir B Mond B D Craven |
| Institution: | 1. Department of Mathematics, Faculty of Military Studies , The University of New South Wales, Royal Military College , Duntroon, Canberra, ACT, 2600, Australia;2. Department of Mathematics , La Trobe University , Bundoora, Victoria, 3083, Australia;3. Department of Mathematics , University of Melbourne , Parkville, Victoria, 3052, Australia |
| Abstract: | Sufficient and necessary optimality conditions are given for weakly minimized optimization problems in terms of a vector valued Lagrangian. Lagrangian and Wolfe type duals are constructed and duality established using an ordering that accords with the definition of a weak minimum. The results for differentiable problems continue to hold under weakened convexity assumptions and for problems which quasiminimize rather than minimize. |
| Keywords: | Approximatively compact set upper semi-continuous map almost affine map |