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Overview
The book includes:
- Derivative-based Methods of Optimization.
- Direct Search Methods of Optimization.
- Basics of Riemannian Differential Geometry.
- Geometric Methods of Optimization using Riemannian Langevin Dynamics.
- Stochastic Analysis on Manifolds and Geometric Optimization Methods.
This textbook comprehensively treats both classical and geometric optimization methods, including deterministic and stochastic (Monte Carlo) schemes. It offers an extensive coverage of important topics including derivative-based methods, penalty function methods, method of gradient projection, evolutionary methods, geometric search using Riemannian Langevin dynamics and stochastic dynamics on manifolds. The textbook is accompanied by online resources including MATLAB codes which are uploaded on our website. The textbook is primarily written for senior undergraduate and graduate students in all applied science and engineering disciplines and can be used as a main or supplementary text for courses on classical and geometric optimization.
Product Details
ISBN-13: | 9780367560164 |
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Publisher: | CRC Press |
Publication date: | 01/25/2024 |
Pages: | 524 |
Product dimensions: | 6.12(w) x 9.19(h) x (d) |
About the Author
G. Visweswara Rao is currently working as an engineering consultant in Bangalore, India. He received his Ph.D. from the Indian Institute of Science, Bangalore, in 1989. He has published several research papers in the areas of structural dynamics specific to earthquake engineering, nonlinear and random vibration, and structural control. His areas of research include non-linear and stochastic structural dynamics.
Table of Contents
ContentsChapter 1 Optimization methods – A preview
1.1 Introduction
1.2 The continuous case – mathematical formulation
1.3 The discrete case – The travelling salesman problem
1.4 Basics of probability theory and random number generation
1.5 The brachistochrone problem
1.6 More on functional optimization: Hamilton’s principle
1.7 Constrained optimization problems and optimality conditions
1.8. Functional optimization and optimal control
Concluding Remarks
Exercises
Notations
References
Chapter 2 Classical derivative-based methods of optimization
2.1 Introduction
2.2 Basic gradient methods
2.3 Quasi-Newton methods
2.4 Penalty function methods
2.5 Linear programming (LP)
2.6. Method of generalized reduced gradients
2.7 Method of feasible directions
2.8 Method of gradient projection
Concluding remarks
Exercises
Notations
References
Chapter 3 – Classical derivative-free methods of optimization
3.1 Introduction
3.2 Direct search methods
3.3 Other direct search methods
3.4 Metaheuristics - Evolutionary methods
Concluding remarks
Exercises
Notations
References
Chapter 4 Elements of Riemannian Differential Geometry and geometric methods of optimization
4.1 Introduction
4.2 Tangent vectors and tangent space on manifolds
4.3 Riemannian (geometric) version of some classical gradient methods
4.4. Statistical estimation by geometrical method of optimization
4.5. Stochastic processes, stochastic calculus and solution of SDEs
4.6. Analogy between statistical sampling and stochastic optimization
4.7. Geometric method of optimization by Riemannian Langevin dynamics
Concluding remarks
Exercises
Notations
References
Chapter 5 Stochastic analysis on a manifold and more on geometric optimization methods
5.1. Introduction
5.2 Stochastic development on a manifold
5.3. Non-convex function optimization based on stochastic development
5.4. Parameter estimation by GALA
Concluding remarks
Notations
References