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Relative Optimization of Continuous-Time and Continuous-State Stochastic Systems

Name: Relative Optimization of Continuous-Time and Continuous-State Stochastic Systems
Brand: Springer, Berlin
SKU: 9783030418458
Price: 57766 HUF
Availability: InStock

Szerző: Xi-Ren Cao

Nyelv:

Kötés: Kemény kötésű

Kiadó: Springer, Berlin

Elérhetőség: Beszállítói készleten

Küldés 10-13 napon belül

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This monograph applies the relative optimization approach to time nonhomogeneous continuous-time and...

Információk a könyvről

Szerző

Xi-Ren Cao

Nyelv

Angol

Kötés

Könyv - Kemény kötésű

Kiadva

2020

oldal

365

EAN

9783030418458

Enbook ID

25610120

Kiadó

Springer, Berlin

Súly

680

Méretek

159 x 24 x 25

Teljes leírás

This 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. The 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. Among the more important novel considerations presented are: the 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; proof of semi-smoothness of the value function at degenerate points; attention to the under-selectivity issue for the long-run average and bias optimality; and discussion of state classification for time nonhomogeneous continuous processes and multi-class optimization development 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. The book will be of interest to researchers and students in the field of stochastic control and performance optimization alike.