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.
Biography
Rajesh Kumar Arora is a senior engineer at the Indian Space Research Organization, where he has been working for more than two decades. He obtained his PhD in aerospace engineering from the Indian Institute of Science, Bangalore. His research interests include mission design, simulation of launch vehicle systems, and trajectory optimization.
Arora (senior engineer, Indian Space Research Organization) has written a textbook on linear and nonlinear optimization that might be used in an advanced undergraduate- or graduate-level introductory course in optimization for students in engineering and science. The book's 11 chapters discuss topics such as linear and integer programming, unconstrained and constrained nonlinear programming, multiobjective optimization, and geometric programming. This is a broad range of subjects, but many are introduced only briefly. For example, the author covers the important topic of interior point methods for linear programming in a single two-page section. Most exercises are simple computations, and there are few theoretical exercises. Arora includes sample MATLAB codes for solving many of the examples in the text. (...)
--B. Borchers, New Mexico Institute of Mining and Technology
