Titlebook: Constructive Nonsmooth Analysis and Related Topics; Vladimir F. Demyanov,Panos M. Pardalos,Mikhail Bat Book 2014 Springer Science+Business

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Alternance Form of Optimality Conditions in the Finite-Dimensional Space,a point under study satisfies the conditions, and, secondly, if it does not, to find a “better” point. This is why such conditions should be “constructive” letting to solve the above-mentioned problems. For the class of directionally differentiable functions in . ., a necessary condition for an unco

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Optimal Multiple Decision Statistical Procedure for Inverse Covariance Matrix,tistical procedure is given. This procedure is constructed using the Lehmann theory of multiple decision statistical procedures and the conditional tests of the Neyman structure. The equations for thresholds calculation for the tests of the Neyman structure are analyzed.

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https://doi.org/10.1007/978-3-642-10663-7arest to the origin. If the origin does not belong to ., we easily find the steepest descent direction and are able to construct a numerical method. For the classical Chebyshev approximation problem (the problem of approximating a function .(.): . → . by a polynomial .(.)), the condition for a minim

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Alternance Form of Optimality Conditions in the Finite-Dimensional Space,arest to the origin. If the origin does not belong to ., we easily find the steepest descent direction and are able to construct a numerical method. For the classical Chebyshev approximation problem (the problem of approximating a function .(.): . → . by a polynomial .(.)), the condition for a minim

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1931-6828 ributes to three giants of nonsmooth analysis, convexity, and optimization: Alexandr Alexandrov, Leonid Kantorovich, and Alex Rubinov. The last chapter provides an overview and important snapshots of the 50-year history of convex analysis and optimization..978-1-4939-4631-0978-1-4614-8615-2Series ISSN 1931-6828 Series E-ISSN 1931-6836

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Constructive Nonsmooth Analysis and Related Topics

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Separable Reduction of Metric Regularity Properties,a separable subspace . ⊂ . containing . . such that the mapping whose graph is the intersection of the graph of . with . × . (restriction of . to . × .) is metrically regular near the same point. Moreover, it is shown that the rates of regularity of the mapping near the point can be recovered from the rates of such restrictions.