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Last update: T_KPMS (09.05.2014)
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Last update: T_KPMS (25.04.2016)
(i) Lecture builds up fundaments of variation geometry and of calculus for nonsmooth singlevalued and multivalued mappings. The main task is to develop the generalized differential calculus of the first and the second order, variational principles and stability theory of multivalued mappings.
(ii) The theory is applied to particular problems of optimization and game theory. The considered problems belong to generalized problems of mathematical programming, variational and quasi-variational inequalities, noncooperative equilibria and games with hierarchic structure. |
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Last update: T_KPMS (09.05.2014)
[1] B.S. Mordukhovich: Variational Analysis and Generalized Differentiation, Vol. 1: Basic Theory, Vol. 2: Applications, Springer, Berlin, 2006. [2] R. T. Rockafellar: Applications of convex variational analysis to Nash equilibrium, Proceedings of 7th International Conference on Nonlinear Analysis and Convex Analysis (Busan, Korea, 2011), 173-183. [3] R.T. Rockafellar, R. J.-B. Wets: Variational Analysis, Springer, Berlin 1998. [4] W. Schirotzek: Nonsmooth Analysis, Springer, Berlin, 2007. |
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Last update: T_KPMS (09.05.2014)
Lecture. |
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Last update: T_KPMS (09.05.2014)
Nonconvex nonsmooth analysis 1) Variational geometry nonconvex sets. (Several types of normal cones and their relations). 2) Subdiferentials and coderivatives (Fréchet, proximal, Clarke, Mordukhovich). 3) First order calculus with relaxed constraint qualification based on chain rules. 4) Second order calculus (derivatives of compositions for polyhedral and conic constraint systems). 5) Applications: Optimality conditions, stability analysis of multifunction, error bound property, nonsmooth numerical methods. |