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Optimization and nonsmooth analysis
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TLDR
The Calculus of Variations as discussed by the authors is a generalization of the calculus of variations, which is used in many aspects of analysis, such as generalized gradient descent and optimal control.Abstract:
1. Introduction and Preview 2. Generalized Gradients 3. Differential Inclusions 4. The Calculus of Variations 5. Optimal Control 6. Mathematical Programming 7. Topics in Analysis.read more
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Journal ArticleDOI
Decomposition algorithms for generalized potential games
TL;DR: This work analyzes some new decomposition schemes for the solution of generalized Nash equilibrium problems and proves convergence for a particular class of generalized potential games that includes some interesting engineering problems.
Proceedings Article
Structure estimation for discrete graphical models: Generalized covariance matrices and their inverses
Po-Ling Loh,Martin J. Wainwright +1 more
TL;DR: In this article, the authors investigated the relationship between the structure of a discrete graphical model and the support of the inverse of a generalized covariance matrix and showed that for certain graph structures, the correlation between the inverse matrix of indicator variables on the vertices of a graph reflects the conditional independence structure of the graph.
Journal ArticleDOI
Calmness and exact penalization
TL;DR: In this article, the notion of calmness, introduced by Clarke and Rockafellar for constrained optimization, is considered and an equivalence to the technique of exact penalization due to Eremin and Zangwill is established.
Journal ArticleDOI
Löwner's Operator and Spectral Functions in Euclidean Jordan Algebras
Defeng Sun,Jie Sun +1 more
TL;DR: It is shown that many optimization-related classical results in the symmetric matrix space can be generalized within this framework and the metric projection operator over any symmetric cone defined in a Euclidean Jordan algebra is shown to be strongly semismooth.
Journal ArticleDOI
Distributed convergence to Nash equilibria in two-network zero-sum games
TL;DR: In this article, the authors considered a class of strategic scenarios in which two networks of agents have opposing objectives with regard to the optimization of a common objective function and synthesized a distributed saddle-point strategy and established its convergence to the Nash equilibrium for the class of strictly concaveconvex and locally Lipschitz objective functions.