| Abstract: |
| Aim of the talk is to discuss and refine strong duality theory in infinite-dimensional settings. In particular, we deal with three constraint qualification conditions, Assumption S, Assumption S`, and Condition NES, which are necessary and sufficient conditions for strong duality, highlighting their relationship with the saddle points of the Lagrange functional and the equivalence with a global optimization problem.
Moreover, these assumptions prove to be very useful in many applications. Indeed, many equilibrium problems may be expressed in terms of variational or quasi-variational inequalities, in which these assumptions work. In the talk, in particular, we apply strong duality theory to the existence of Lagrange multipliers in the difficult partial differential equations setting of non-constant gradient constrained problem. |
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