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