Moments, Positive Polynomials and Their Applications pdf epub mobi txt 电子书下载 2024

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Lasserre, Jean-Bernard

2009-10

300

769.00元

9781848164451

图书标签: 不等式

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发表于2024-12-29

Moments, Positive Polynomials and Their Applications epub 下载 mobi 下载 pdf 下载 txt 电子书下载 2024

Moments, Positive Polynomials and Their Applications pdf epub mobi txt 电子书下载 2024

图书描述

Many important problems in global optimization, algebra, probability and statistics, applied mathematics, control theory, financial mathematics, inverse problems, etc. can be modeled as a particular instance of the Generalized Moment Problem (GMP). This book introduces, in a unified manual, a new general methodology to solve the GMP when its data are polynomials and basic semi-algebraic sets. This methodology combines semidefinite programming with recent results from real algebraic geometry to provide a hierarchy of semidefinite relaxations converging to the desired optimal value. Applied on appropriate cones, standard duality in convex optimization nicely expresses the duality between moments and positive polynomials. In the second part of this invaluable volume, the methodology is particularized and described in detail for various applications, including global optimization, probability, optimal context, mathematical finance, multivariate integration, etc., and examples are provided for each particular application.

Moments, Positive Polynomials and Their Applications 下载 mobi epub pdf txt 电子书