[...]... 4.6 .1 Convex Sets 4.6.2 Convex Functions 4.6.3 Convex Programming Problem 4.6.4 Transformation of a Constraint 4.6.5 Sufficient Conditions for Convex Programming Problems 4.7 Engineering Design Examples 4.7 .1 Design of a Wall Bracket 4.7.2 Design of a Rectangular Beam Exercises for Chapter 4 Chapter 5 10 3 10 3 10 4 10 9 11 6 11 9 11 9 12 1 12 8 14 0 14 1 14 3 14 3 14 6 14 7 14 8 14 9 14 9 15 1 15 3 15 6 15 7 15 8 15 8 16 2 16 6... 404 406 406 407 407 409 410 411 Contents 413 12 .1 xvi Introduction to Optimum Design with MATLAB 413 413 Introduction to Optimization Toolbox 12 .1. 1 Variables and Expressions 12 .1. 2 Scalar, Array, and Matrix Operations 12 .1. 3 Optimization Toolbox 12 .2 Unconstrained Optimum Design Problems 12 .3 Constrained Optimum Design Problems 12 .4 Optimum Design Examples with MATLAB 12 .4 .1 Location of Maximum Shear... Method 17 .9 Goal Programming 17 .10 Selection of Methods Exercises for Chapter 17 Chapter 18 Multiobjective Optimum Design Concepts and Methods 17 .1 17.2 Chapter 17 538 539 540 543 546 546 548 5 51 5 51 5 51 552 552 552 555 556 556 558 558 559 559 560 Global Optimization Concepts and Methods for Optimum Design 565 18 .1 18.2 18 .3 18 .4 18 .5 Basic Concepts of Solution Methods 18 .1. 1 Basic Concepts 18 .1. 2 Overview... Problem 11 .2 .1 Definition of QP Problem 11 .2.2 KKT Necessary Conditions for the QP Problem 11 .2.3 Transformation of KKT Conditions 11 .2.4 Simplex Method for Solving QP Problem 11 .3 Approximate Step Size Determination 11 .3 .1 The Basic Idea 11 .3.2 Descent Condition 11 .3.3 CSD Algorithm with Approximate Step Size 11 .4 Constrained Quasi-Newton Methods 11 .4 .1 Derivation of Quadratic Programming Subproblem 11 .4.2... 18 .5.4 Global Optimization of Structural Design Problems Exercises for Chapter 18 Appendix A 586 587 588 Time Value of Money A .1. 1 Cash Flow Diagrams A .1. 2 Basic Economic Formulas A.2 Economic Bases for Comparison A.2 .1 Annual Base Comparisons A.2.2 Present Worth Comparisons Exercises for Appendix A 611 611 613 613 613 613 613 615 616 616 616 616 617 618 618 619 6 21 625 628 628 629 635 635 639 642 643... Contact 12 .4.2 Column Design for Minimum Mass 12 .4.3 Flywheel Design for Minimum Mass Exercises for Chapter 12 420 4 21 425 429 Interactive Design Optimization 433 13 .1 Chapter 13 434 434 Role of Interaction in Design Optimization 13 .1. 1 What Is Interactive Design Optimization? 13 .1. 2 Role of Computers in Interactive Design Optimization 13 .1. 3 Why Interactive Design Optimization? 13 .2 Interactive Design. .. Methods 9.7 .1 Sequential Unconstrained Minimization Techniques 9.7.2 Multiplier (Augmented Lagrangian) Methods Exercises for Chapter 9 Chapter 10 305 306 309 310 310 314 315 318 318 319 323 Numerical Methods for Constrained Optimum Design 339 10 .1 340 Basic Concepts and Ideas 10 .1. 1 Basic Concepts Related to Algorithms for Constrained Problems 10 .1. 2 Constraint Status at a Design Point 10 .1. 3 Constraint... The Design Process Engineering Design versus Engineering Analysis Conventional versus Optimum Design Process Optimum Design versus Optimal Control Basic Terminology and Notation 1. 5 .1 Sets and Points 1. 5.2 Notation for Constraints 1. 5.3 Superscripts/Subscripts and Summation Notation 1. 5.4 Norm/Length of a Vector 1. 5.5 Functions 1. 5.6 U.S.-British versus SI Units 1 2 4 4 6 7 7 9 9 11 11 12 Optimum Design. .. Chapter 15 xviii Contents Genetic Algorithms for Optimum Design 5 31 16 .1 16.2 Chapter 16 514 515 516 517 519 520 5 21 522 522 524 525 525 526 527 532 534 Basic Concepts and Definitions Fundamentals of Genetic Algorithms 514 16 .3 Genetic Algorithm for Sequencing-Type Problems 16 .4 Applications Exercises for Chapter 16 543 Problem Definition Terminology and Basic Concepts 17 .2 .1 Criterion Space and Design. .. Truss 2 .11 A General Mathematical Model for Optimum Design 2 .11 .1 Standard Design Optimization Model 2 .11 .2 Maximization Problem Treatment 2 .11 .3 Treatment of “Greater Than Type” Constraints 2 .11 .4 Discrete and Integer Design Variables 2 .11 .5 Feasible Set 2 .11 .6 Active/Inactive/Violated Constraints Exercises for Chapter 2 Graphical Optimization 55 3 .1 Chapter 3 32 33 34 35 36 55 55 56 60 61 Graphical . 410 Exercises for Chapter 11 411 Chapter 12 Introduction to Optimum Design with MATLAB 413 12 .1 Introduction to Optimization Toolbox 413 12 .1. 1 Variables and Expressions 413 xvi Contents 12 .1. 2 Scalar, Array,. Operations 414 12 .1. 3 Optimization Toolbox 414 12 .2 Unconstrained Optimum Design Problems 415 12 .3 Constrained Optimum Design Problems 418 12 .4 Optimum Design Examples with MATLAB 420 12 .4 .1 Location. 508 Chapter 15 Discrete Variable Optimum Design Concepts and Methods 513 15 .1 Basic Concepts and Definitions 514 15 .1. 1 Definition of Mixed Variable Optimum Design Problem: MV-OPT 514 15 .1. 2 Classification