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portada Relative Optimization of Continuous-Time and Continuous-State Stochastic Systems
Type
Physical Book
Author
Publisher
Language
English
Pages
365
Format
Paperback
Dimensions
23.4x15.6x2 cm
Weight
0.54 kg.
ISBN13
9783030418489
Categories

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

Xi-Ren Cao (Author) · Springer · Paperback

Relative Optimization of Continuous-Time and Continuous-State Stochastic Systems - Cao, XI-Ren

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

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; anddevelopment 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 andperformance optimization alike.

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