Titlebook: Optimization Theory; Recent Developments Franco Giannessi,Panos Pardalos,Tamás Rapcsák Book 20011st edition Kluwer Academic Publishers 200

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Optimization Theory978-1-4613-0295-7Series ISSN 1384-6485

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Lower and Upper Bounds on the Probability of the Union of Some Events with Applications,Lower and upper bounds on the probability of the union of some events are presented. The bounds are based on special hypergraphs called (.,)-hyper-multitrees. A new probability bounding technique based on the bounds is described and it is applied to estimate the value of multivariate normal distribution functions.

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Convexification of Functions by Nonlinear Coordinate Transformations,The convexification of continuous and smooth functions are related to the choice of Riemannian metrics originated from regular nonlinear coordinate transformations.

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,Packing Equal Circles in a Square I. — Problem Setting and Bounds for Optimal Solutions,this problem defined on the basis of regular arrangements. Also, there will new upper bounds be established based on the computation of the areas of circle and minimum gap between circles and between circles and sides of the square. The paper also contains all the known exact values of optimal packings and the corresponding minimal polynomials.

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https://doi.org/10.1007/978-1-4613-0295-7algorithms; Approximation; calculus; computer; inequality; Mathematica; operations research; optimization; p

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