• 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 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
• 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