V úterý 24. června se na UMAT konala přednáška prof. Galewského z Institute of Mathematics, Faculty of Technical Physics, Information Technology and Applied Mathematics, Technical University of Łódz na téma
The Karush-Kuhn-Tucker Theorem applied to fixed points and zeros of nonlinear maps.
Abstract: In this talk, we explore the existence of fixed points and zeros of certain potential mappings by applying the Lagrange Multiplier Rule and the Karush-Kuhn-Tucker Theorem. By imposing the potentiality requirement on the mapping under consideration, we can significantly simplify the proof using optimization arguments and relax the invariance assumptions. Through these arguments, we derive a version of the Brouwer Lemma and the Schauder Theorem, supplemented by the Krasnosel’skii fixed-point theorem. Due to the nature of the arguments used in the proofs, we restrict our consideration to maps on balls when seeking fixed points and zeros, and to annular domains when investigating the existence of zeros.
Přednáška proběhla v rámci studijního pobytu prof. Galewského na našem ústavu.
