{"title":"Xi-Ren Cao","description":null,"products":[{"product_id":"stochastic-learning-and-optimization-book-xi-ren-cao-9781441942227","title":"Stochastic Learning and Optimization","description":"Performance optimization is vital in the design and operation of modern engineering systems, including communications, manufacturing, robotics, and logistics. 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The topics covered have the following distinguishing features: long-run average with no under-selectivity, non-smooth value functions with no viscosity solutions, diffusion processes with degenerate points, multi-class optimization with state classification, and optimization with no dynamic programming.\u003c\/p\u003e\u003cp\u003eThe book begins with an introduction to relative optimization, including a comparison with the traditional approach of dynamic programming. The text then studies the Markov process, focusing on infinite-horizon optimization problems, and moves on to discuss optimal control of diffusion processes with semi-smooth value functions and degenerate points, and optimization of multi-dimensional diffusion processes. The book concludes with a brief overview of performance derivative-based optimization.\u003c\/p\u003e\u003cp\u003eAmong the more important novel considerations presented are:\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003ethe extension of the Hamilton–Jacobi–Bellman optimality condition from smooth to semi-smooth value functions by derivation of explicit optimality conditions at semi-smooth points and application of this result to degenerate and reflected processes;\u003c\/li\u003e\n\u003cli\u003eproof of semi-smoothness of the value function at degenerate points;\u003c\/li\u003e\n\u003cli\u003eattention to the under-selectivity issue for the long-run average and bias optimality; \u003c\/li\u003e\n\u003cli\u003ediscussion of state classification for time nonhomogeneous continuous processes and multi-class optimization; and\u003c\/li\u003e\n\u003cli\u003edevelopment of the multi-dimensional Tanaka formula for semi-smooth functions and application of this formula to stochastic control of multi-dimensional systems with degenerate points.\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eThe book will be of interest to researchers and students in the field of stochastic control andperformance optimization alike.\u003c\/p\u003e","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52482975039761,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52482976022801,"sku":"NLS9783030418489","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783030418489.jpg?v=1759854021"},{"product_id":"stochastic-learning-and-optimization-book-xi-ren-cao-9780387367873","title":"Stochastic Learning and Optimization","description":"Performance optimization is vital in the design and operation of modern engineering systems. 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However, some recent research indicates that the evolution of these man-made systems demonstrates dynamic features that are similar to those of natural physical systems. This monograph presents a multidisciplinary approach to the study of discrete event systems, and is complementary to textbooks in queuing and control systems theories.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52673744535825,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52673745322257,"sku":"NLS9783540198727","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783540198727.jpg?v=1762297837"},{"product_id":"foundations-of-average-cost-nonhomogeneous-controlled-markov-chains-book-xi-ren-cao-9783030566777","title":"Foundations of Average-Cost Nonhomogeneous Controlled Markov Chains","description":"Using confluencity and relative optimization, the author classifies states as confluent or branching and shows how the under-selectivity issue of the long-run average can be easily addressed, multi-class optimization implemented, and Nth biases and Blackwell optimality conditions derived.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52684449218833,"sku":"NLS9783030566777","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783030566777.jpg?v=1786615959"}],"url":"https:\/\/www.worldofbooks.com\/en-gb\/collections\/author-books-by-xi-ren-cao.oembed","provider":"World of Books ","version":"1.0","type":"link"}