Table of Contents

  • 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

 

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