{"product_id":"relative-optimization-of-continuous-time-and-continuous-state-stochastic-systems-9783030418458","title":"Relative Optimization of Continuous-Time and Continuous-State Stochastic Systems","description":"\u003cp\u003e • Author(s): Xi-Ren Cao\u003cbr\u003e • Publisher: Springer\u003cbr\u003e • Publisher Imprint: Springer\u003cbr\u003e • BISAC: Automation\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003eFrom the Back Cover\u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e\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 \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 \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 \u003cli\u003eproof of semi-smoothness of the value function at degenerate points;\u003c\/li\u003e \u003cli\u003eattention to the under-selectivity issue for the long-run average and bias optimality;\u003c\/li\u003e \u003cli\u003ediscussion of state classification for time nonhomogeneous continuous processes and multi-class optimization; and\u003c\/li\u003e \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 and performance optimization alike.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e","brand":"Springer","offers":[{"title":"Hardcover","offer_id":45276862349463,"sku":"9783030418458","price":10915.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9783030418458.webp?v=1769286858","url":"https:\/\/atlanticbooks.com\/products\/relative-optimization-of-continuous-time-and-continuous-state-stochastic-systems-9783030418458","provider":"Atlantic Books","version":"1.0","type":"link"}