1,051 research outputs found
Rated Extremal Principles for Finite and Infinite Systems
In this paper we introduce new notions of local extremality for finite and
infinite systems of closed sets and establish the corresponding extremal
principles for them called here rated extremal principles. These developments
are in the core geometric theory of variational analysis. We present their
applications to calculus and optimality conditions for problems with infinitely
many constraints
Applying Metric Regularity to Compute a Condition Measure of a Smoothing Algorithm for Matrix Games
We develop an approach of variational analysis and generalized
differentiation to conditioning issues for two-person zero-sum matrix games.
Our major results establish precise relationships between a certain condition
measure of the smoothing first-order algorithm proposed by Gilpin et al.
[Proceedings of the 23rd AAAI Conference (2008) pp. 75-82] and the exact bound
of metric regularity for an associated set-valued mapping. In this way we
compute the aforementioned condition measure in terms of the initial matrix
game data
Tangential Extremal Principles for Finite and Infinite Systems of Sets, II: Applications to Semi-infinite and Multiobjective Optimization
This paper contains selected applications of the new tangential extremal
principles and related results developed in Part I to calculus rules for
infinite intersections of sets and optimality conditions for problems of
semi-infinite programming and multiobjective optimization with countable
constraint
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