Engineering Optimization Theory and Practice

Abstract

Preface. 1 Introduction to Optimization. 1.1 Introduction. 1.2 Historical Development. 1.3 Engineering Applications of Optimization. 1.4 Statement of an Optimization Problem. 1.5 Classification of Optimization Problems. 1.6 Optimization Techniques. 1.7 Engineering Optimization Literature. 1.8 Solution of Optimization Problems Using MATLAB. References and Bibliography. Review Questions. Problems. 2 Classical Optimization Techniques. 2.1 Introduction. 2.2 Single-Variable Optimization. 2.3 Multivariable Optimization with No Constraints. 2.4 Multivariable Optimization with Equality Constraints. 2.5 Multivariable Optimization with Inequality Constraints. 2.6 Convex Programming Problem. References and Bibliography. Review Questions. Problems. 3 Linear Programming I: Simplex Method. 3.1 Introduction. 3.2 Applications of Linear Programming. 3.3 Standard Form of a Linear Programming Problem. 3.4 Geometry of Linear Programming Problems. 3.5 Definitions and Theorems. 3.6 Solution of a System of Linear Simultaneous Equations. 3.7 Pivotal Reduction of a General System of Equations. 3.8 Motivation of the Simplex Method. 3.9 Simplex Algorithm. 3.10 Two Phases of the Simplex Method. 3.11 MATLAB Solution of LP Problems. References and Bibliography. Review Questions. Problems. 4 Linear Programming II: Additional Topics and Extensions. 4.1 Introduction. 4.2 Revised Simplex Method. 4.3 Duality in Linear Programming. 4.4 Decomposition Principle. 4.5 Sensitivity or Postoptimality Analysis. 4.6 Transportation Problem. 4.7 Karmarkar's Interior Method. 4.8 Quadratic Programming. 4.9 MATLAB Solutions. References and Bibliography. Review Questions. Problems. 5 Nonlinear Programming I: One-Dimensional Minimization Methods. 5.1 Introduction. 5.2 Unimodal Function. ELIMINATION METHODS. 5.3 Unrestricted Search. 5.4 Exhaustive Search. 5.5 Dichotomous Search. 5.6 Interval Halving Method. 5.7 Fibonacci Method. 5.8 Golden Section Method. 5.9 Comparison of Elimination Methods. INTERPOLATION METHODS. 5.10 Quadratic Interpolation Method. 5.11 Cubic Interpolation Method. 5.12 Direct Root Methods. 5.13 Practical Considerations. 5.14 MATLAB Solution of One-Dimensional Minimization Problems. References and Bibliography. Review Questions. Problems. 6 Nonlinear Programming II: Unconstrained Optimization Techniques. 6.1 Introduction. DIRECT SEARCH METHODS. 6.2 Random Search Methods. 6.3 Grid Search Method. 6.4 Univariate Method. 6.5 Pattern Directions. 6.6 Powell's Method. 6.7 Simplex Method. INDIRECT SEARCH (DESCENT) METHODS. 6.8 Gradient of a Function. 6.9 Steepest Descent (Cauchy) Method. 6.10 Conjugate Gradient (Fletcher-Reeves) Method. 6.11 Newton's Method. 6.12 Marquardt Method. 6.13 Quasi-Newton Methods. 6.14 Davidon-Fletcher-Powell Method. 6.15 Broyden-Fletcher-Goldfarb-Shanno Method. 6.16 Test Functions. 6.17 MATLAB Solution of Unconstrained Optimization Problems. References and Bibliography. Review Questions. Problems. 7 Nonlinear Programming III: Constrained Optimization Techniques. 7.1 Introduction. 7.2 Characteristics of a Constrained Problem. DIRECT METHODS. 7.3 Random Search Methods. 7.4 Complex Method. 7.5 Sequential Linear Programming. 7.6 Basic Approach in the Methods of Feasible Directions. 7.7 Zoutendijk's Method of Feasible Directions. 7.8 Rosen's Gradient Projection Method. 7.9 Generalized Reduced Gradient Method. 7.10 Sequential Quadratic Programming. INDIRECT METHODS. 7.11 Transformation Techniques. 7.12 Basic Approach of the Penalty Function Method. 7.13 Interior Penalty Function Method. 7.14 Convex Programming Problem. 7.15 Exterior Penalty Function Method. 7.16 Extrapolation Techniques in the Interior Penalty Function Method. 7.17 Extended Interior Penalty Function Methods. 7.18 Penalty Function Method for Problems with Mixed Equality and Inequality Constraints. 7.19 Penalty Function Method for Parametric Constraints. 7.20 Augmented Lagrange Multiplier Method. 7.21 Checking the Convergence of Constrained Optimization Problems. 7.22 Test Problems. 7.23 MATLAB Solution of Constrained Optimization Problems. References and Bibliography. Review Questions. Problems. 8 Geometric Programming. 8.1 Introduction. 8.2 Posynomial. 8.3 Unconstrained Minimization Problem. 8.4 Solution of an Unconstrained Geometric Programming Program Using Differential Calculus. 8.5 Solution of an Unconstrained Geometric Programming Problem Using Arithmetic-Geometric Inequality. 8.6 Primal-Dual Relationship and Sufficiency Conditions in the Unconstrained Case. 8.7 Constrained Minimization. 8.8 Solution of a Constrained Geometric Programming Problem. 8.9 Primal and Dual Programs in the Case of Less-Than Inequalities. 8.10 Geometric Programming with Mixed Inequality Constraints. 8.11 Complementary Geometric Programming. 8.12 Applications of Geometric Programming. References and Bibliography. Review Questions. Problems. 9 Dynamic Programming. 9.1 Introduction. 9.2 Multistage Decision Processes. 9.3 Concept of Suboptimization and Principle of Optimality. 9.4 C