{"product_id":"relative-optimization-of-continuous-time-and-continuous-state-stochastic-systems-von-xi-ren-cao","title":"Relative Optimization of Continuous-Time and Continuous-State Stochastic Systems","description":"\n                                \n                \u003cp\u003eThis monograph applies the relative optimization approach to time nonhomogeneous continuous-time and continuous-state dynamic systems. The approach is intuitively clear and does not require deep knowledge of the mathematics of partial differential equations. 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\n                                \n                \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\n                                \n                \u003cp\u003eAmong the more important novel considerations presented are:\u003c\/p\u003e\n                                \n                \u003cul\u003e\n                                        \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                                        \n                    \u003cli\u003eproof of semi-smoothness of the value function at degenerate points;\u003c\/li\u003e\n                                        \n                    \u003cli\u003eattention to the under-selectivity issue for the long-run average and bias optimality; \u003c\/li\u003e\n                                        \n                    \u003cli\u003ediscussion of state classification for time nonhomogeneous continuous processes and multi-class optimization; and\u003c\/li\u003e\n                                        \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                                    \n                \u003c\/ul\u003e\n                                \n                \u003cp\u003eThe book will be of interest to researchers and students in the field of stochastic control andperformance optimization alike.\u003c\/p\u003e\n                            \n            \u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783030418489\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783030418458\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e","brand":"Libri","offers":[{"title":"Softcover - 9783030418489","offer_id":39418920796253,"sku":"9783030418489","price":160.49,"currency_code":"EUR","in_stock":true},{"title":"Hardcover - 9783030418458","offer_id":39784288125021,"sku":"9783030418458","price":160.49,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/3a0355de-f72f-4cd1-ab05-0740f46f0a64.jpg?v=1778733547","url":"https:\/\/shop.autorenwelt.de\/en\/products\/relative-optimization-of-continuous-time-and-continuous-state-stochastic-systems-von-xi-ren-cao","provider":"Autorenwelt Shop","version":"1.0","type":"link"}