Table Of Contents
Preface
Before You Begin
Chapter I
INTRODUCTION
Perspective
Formulation of Optimization Problems
Topics in Optimization
Method of Attack
Summary
References
Chapter II
CLASSICAL THEORY OF MAXIMA AND MINIMA
Introduction
Analytical Methods without Constraints
Locating Local Maxima and Minima (Necessary Conditions)
Evaluating Local Maxima and Minima (Sufficient Conditions)
Sufficient Conditions for One Independent Variables
Sufficient Conditions for Two Independent Variables
Sign of a Quadratic Form
Sufficient Conditions for N Independent Variables
Analytical Methods Applicable for Constraints
Direct Substitution
Constrained Variation
Lagrange Multipliers
Method of Steepest Ascent
Economic Interpretation of the Lagrange Multipliers
Inequality Constraints
Necessary and Sufficient Conditions for Constrained Problems
Closure
References
Problems
Chapter III
GEOMETRIC PROGRAMMING
Introduction
Optimization of Posynomials
Optimization of Polynomials
Closure
References
Problems
Chapter IV
LINEAR PROGRAMMING
Introduction
Concepts and Methods
Concepts and Geometric Interpretation
General Statement of the Linear Programming Problem
Slack and Surplus Variables
Feasible and Basic Feasible Solutions of the Constraint Equations
Optimization with the Simplex Method
Simplex Tableau
Mathematics of Linear Programming
Degeneracy
Artificial Variables
Formulating and Solving Problems
Formulating the Linear Programming Problem-A Simple Refinery
Solving the Linear Programming Problem for the Simple Refinery
Sensitivity Analysis
Changes in the Right Hand Side of the Constraint Equation
Changes in the Coefficients of the Objective Function
Changes in the Coefficients of the Constraint Equations
Addition of New Variables
Addition of More Constraint Equations
Closure
Selected List of Texts on Linear Programming and Extensions
References
Problems
Chapter V
SINGLE VARIABLE SEARCH TECHNIQUES
Introduction
Search Problems and Search Plans
Unimodality
Reducing the Interval of Uncertainty
Measuring Search Effectiveness
Minimax Principle
Simultaneous Search Methods
Sequential Search Methods
Fibonacci Search
Golden Section Search
Lattice Search
Open Initial Interval
Other Methods
Closure
References
Problems
Chapter VI
MULTIVARIABLE OPTIMIZATION PROCEDURES
Introduction
Mutivariable Search Methods Overview
Unconstrained Multivariable Search Methods
Quasi-Newton Methods
Conjugate Gradient and Direction Methods
Logical Methods
Constrained Multivariable Search Methods
Successive Linear Programming
Successive Quadratic Programming
Generalized Reduced Gradient Method
Penalty, Barrier and Augmented Lagrangian Functions
Other Multivariable Constrained Search Methods
Comparison of Constrained Multivariable Search Methods
Stochastic Approximation Procedures
Closure
FORTRAN Program for BFGS Search of an Unconstrained Function
References
Problems
Chapter VII
DYNAMIC PROGRAMMING
Introduction
Variables, Transforms, and Stages
Serial System Optimization
Initial Value Problem
Final Value Problem
Two-Point Boundary Value Problem
Cyclic Optimization
Branched Systems
Diverging Branches and Feed Forward Loops
Converging Branches and Feed Back Loops
Procedures and Simplifying Rules
Application to the Contact Process - A Case Study
Brief Description of the Process
Dynamic Programming Analysis
Results
Optimal Equipment Replacement - Time as a Stage
Optimal Allocation by Dynamic Programming
Closure
References
Problems
Chapter VIII
CALCULUS OF VARIATIONS
Introduction
Euler Equation
Functions, Functionals and Neighborhoods
More Complex Problems
Functional with Higher Derivatives in the Integrand
Functional with Several Functions in the Integrand
Functional with Several Functions and Higher Derivatives
Functional with More than One Independent Variable
Constrained Variational Problems
Algebraic Constraints
Integral Constraints
Differential Equation Constraints
Closure
References
Problems