{"product_id":"moments-positive-polynomials-and-their-applications-paperback","title":"Moments, Positive Polynomials and Their Applications - Paperback","description":"\u003cdiv\u003e\u003cp style=\"text-align: right;\"\u003e\u003ca href=\"https:\/\/reportcopyrightinfringement.com\/\" target=\"_blank\" rel=\"nofollow\"\u003e\u003cb\u003eReport copyright infringement\u003c\/b\u003e\u003c\/a\u003e\u003c\/p\u003e\u003c\/div\u003e\u003cp\u003eby \u003cb\u003eLasserre Jean Bernard\u003c\/b\u003e (Author)\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eMany important applications 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 \u003cem\u003eGeneralized Moment Problem (GMP)\u003c\/em\u003e.\u003c\/p\u003e \u003cp\u003eThis book introduces 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.\u003c\/p\u003e \u003cp\u003eIn the second part, the methodology is particularized and described in detail for various applications, including global optimization, probability, optimal control, mathematical finance, multivariate integration, etc., and examples are provided for each particular application.\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e\u003ch3\u003eFront Jacket\u003c\/h3\u003e\u003cp\u003eMany 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). \u003c\/p\u003e\u003cp\u003e 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. \u003c\/p\u003e\u003cp\u003e 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.\u003c\/p\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 384\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 0.79 x 9 x 6 IN\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e October 02, 2009\u003c\/div\u003e\n            ","brand":"BooksCloud","offers":[{"title":"Default Title","offer_id":53344385204531,"sku":"9781911299738","price":118.78,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0300\/5595\/6612\/files\/XMKa-Uw1Cp9781911299738.webp?v=1778725336","url":"https:\/\/www.vysn.com\/en-ca\/products\/moments-positive-polynomials-and-their-applications-paperback","provider":"VYSN","version":"1.0","type":"link"}