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Relative optimization of continuous-...

Cao, Xi-Ren.

Relative optimization of continuous-time and continuous-state stochastic systems

Record Type:	Electronic resources : Monograph/item
Title/Author:	Relative optimization of continuous-time and continuous-state stochastic systemsby Xi-Ren Cao.
Author:	Cao, Xi-Ren.
Published:	Cham :Springer International Publishing :2020.
Description:	xix, 365 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Dynamic programming.
Online resource:	https://doi.org/10.1007/978-3-030-41846-5
ISBN:	9783030418465$q(electronic bk.)

Relative optimization of continuous-time and continuous-state stochastic systems
Cao, Xi-Ren.

Relative optimization of continuous-time and continuous-state stochastic systems[electronic resource] /by Xi-Ren Cao. - Cham :Springer International Publishing :2020. - xix, 365 p. :ill., digital ;24 cm. - Communications and control engineering,0178-5354. - Communications and control engineering..

Chapter 1. Introduction -- Chapter 2. Optimal Control of Markov Processes: Inﬁnite Horizon -- Chapter 3. Optimal Control of Diffusion Processes -- Chapter 4. Degenerate Diffusion Processes -- Chapter 5. Multi-Dimensional Diffusion Processes -- Chapter 6. Performance-Derivative-Based Optimization -- Appendices -- Index.

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; discussion of state classification for time nonhomogeneous continuous processes and multi-class optimization; and 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.

ISBN: 9783030418465$q(electronic bk.)

Standard No.: 10.1007/978-3-030-41846-5doiSubjects--Topical Terms:

181912
Dynamic programming.

LC Class. No.: T57.83 / .C369 2020

Dewey Class. No.: 519.703

Relative optimization of continuous-time and continuous-state stochastic systems
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505 0 $a Chapter 1. Introduction -- Chapter 2. Optimal Control of Markov Processes: Inﬁnite Horizon -- Chapter 3. Optimal Control of Diffusion Processes -- Chapter 4. Degenerate Diffusion Processes -- Chapter 5. Multi-Dimensional Diffusion Processes -- Chapter 6. Performance-Derivative-Based Optimization -- Appendices -- Index.
520 $a 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; discussion of state classification for time nonhomogeneous continuous processes and multi-class optimization; and 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.
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