Description

# Optimization

Algorithms and Applications

## Author: Arora Rajesh Kumar

Language: Anglais## Subjects for *Optimization*:

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## Description

/li>## Contents

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*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.*