Optimization
Algorithms and Applications

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Language: Anglais

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· 15.6x23.5 cm · Hardback

Choose the Correct Solution Method for Your Optimization Problem

Optimization: Algorithms and Applications presents a variety of solution techniques for optimization problems, emphasizing concepts rather than rigorous mathematical details and proofs.

The book covers both gradient and stochastic methods as solution techniques for unconstrained and constrained optimization problems. It discusses the conjugate gradient method, Broyden?Fletcher?Goldfarb?Shanno algorithm, Powell method, penalty function, augmented Lagrange multiplier method, sequential quadratic programming, method of feasible directions, genetic algorithms, particle swarm optimization (PSO), simulated annealing, ant colony optimization, and tabu search methods. The author shows how to solve non-convex multi-objective optimization problems using simple modifications of the basic PSO code. The book also introduces multidisciplinary design optimization (MDO) architectures?one of the first optimization books to do so?and develops software codes for the simplex method and affine-scaling interior point method for solving linear programming problems. In addition, it examines Gomory?s cutting plane method, the branch-and-bound method, and Balas? algorithm for integer programming problems.

The author follows a step-by-step approach to developing the MATLAB® codes from the algorithms. He then applies the codes to solve both standard functions taken from the literature and real-world applications, including a complex trajectory design problem of a robot, a portfolio optimization problem, and a multi-objective shape optimization problem of a reentry body. This hands-on approach improves your understanding and confidence in handling different solution methods. The MATLAB codes are available on the book?s CRC Press web page.

Introduction
Historical Review
Optimization Problem
Modeling of the Optimization Problem
Solution with the Graphical Method
Convexity
Gradient Vector, Directional Derivative, and Hessian Matrix
Linear and Quadratic Approximations
Organization of the Book

1-D Optimization Algorithms
Introduction
Test Problem
Solution Techniques
Comparison of Solution Methods

Unconstrained Optimization
Introduction
Unidirectional Search
Test Problem
Solution Techniques
Additional Test Functions
Application to Robotics

Linear Programming
Introduction
Solution with the Graphical Method
Standard Form of an LPP
Basic Solution
Simplex Method
Interior-Point Method
Portfolio Optimization

Guided Random Search Methods
Introduction
Genetic Algorithms
Simulated Annealing
Particle Swarm Optimization
Other Methods

Constrained Optimization
Introduction
Optimality Conditions
Solution Techniques
Augmented Lagrange Multiplier Method
Sequential Quadratic Programming
Method of Feasible Directions
Application to Structural Design

Multiobjective Optimization
Introduction
Weighted Sum Approach
ε-Constraints Method
Goal Programming
Utility Function Method
Application

Geometric Programming
Introduction
Unconstrained Problem
Dual Problem
Constrained Optimization
Application

Multidisciplinary Design Optimization
Introduction
MDO Architecture
MDO Framework
Response Surface Methodology

Integer Programming
Introduction
Integer Linear Programming
Integer Nonlinear Programming

Dynamic Programming
Introduction
Deterministic Dynamic Programming
Probabilistic Dynamic Programming

Bibliography

Appendix A: Introduction to MATLAB
Appendix B: MATLAB Code
Appendix C: Solutions to Chapter Problems

Index

Chapter Highlights, Formula Charts, and Problems appear at the end of each chapter.