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Search Engine Optimization For Dummies, 5th Edition

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Search engine optimization (SEO) is an integral part of getting a site to rank high in the various search engines in order to attract potential customers. With this new edition of a bestseller, you?ll learn the ins and outs and best practices of successful SEO in order to make your website content more search-engine friendly so that it ranks higher among search engines and draws high-volume traffic.

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Search Engine Optimization For Dummies, 5th Edition is the fun and friendly place to start learning how to move your site to the top of the rankings.

Sours: https://www.oreilly.com/library/view/search-engine-optimization/9781118396124/

Engineering Optimization: Theory and Practice, 5th Edition

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    DnD 5e – Character Optimization

    Last Updated: September 24, 2021

    Character optimization, at its simplest, is the act of looking at two choices when building a character and choosing the option which will make your character more mechanically effective. The practice is a bit more nuanced, if only because the abundance of options makes weighing those choices challenging. The collection of articles below includes detailed guidance on building your ideal character from top to bottom.

    State of the Character Optimization Meta

    A discussion of the current state of the character optimization meta, including changes introduced in Tasha’s Cauldron of Everything.

    This article will be periodically updated as new source books are released and rules changes are introduced.

    Classes

    General guides to building and playing your class.

    Races

    Sometimes you want to play a specific race. Knowing which options are available for that race can make playing that race more viable.

    Support Articles

    Sours: https://rpgbot.net/dnd5/characters/
    The Hexblade Warlock - D\u0026D: Optimized #1

    DnD 5e – State of the Character Optimization Meta

    Last Updated: June 20, 2021

    Introduction

    As new source materials are released and those materials are explored, the state the character optimization “meta” changes over time. A basic understanding of the state of the meta will help you a great deal in inderstanding character optimization and articles written about character optimization, including my own.

    Table of Contents

    What is the Meta?

    The “meta” is the current state of affairs in the game with all of the given materials available today. In a practical sense, it’s the state of the world with all of the official published character options available.

    When a new source book is published, the meta changes. New options and rules changes can change the relative usefulness of pre-existing options. For example: new feats like Prodigy and Skill Expert made multiclassing into Rogue to get Expertise less appealing, presenting changes in the character optimization meta.

    Current State of the Meta

    The current meta is defined by Tasha’s Cauldron of Everything. In addition to new subclass options, feats, and spells, Tasha’s introduced a series of optional rules for customizing races and classes which dramatically altered the meta.

    Tasha’s Cauldron of Everything also updates the Artificer class and several spells first introduced in the Sword Coast Adventurer’s Guide, including both Green-Flame Blade and Booming Blade, spells which had a massive impact on the character optimization meta.

    The fact that these are optional rules is immensely frustrating because it means that character optimization efforts may now need to account for games which stick to published racial traits and for games which choose to embrace the rules presented in Tasha’s. It’s also unclear how future races will be designed since Tasha’s doesn’t include any new playable races.

    While these rules are technically “optional”, I believe that it’s likely that groups will adopt the new rules as the new default. DnDBeyond lists the ability to replace ability score increases in entries for racial traits and makes no mention of the fact that the rule is optional. The official Adventurer’s League organized play group has already embraced the optional rules (check the Tasha’s Cauldron of Everything Guidance document), and I suspect that many home play groups will do the same. Only time will tell.

    Races

    Tasha’s introduced two major changes to how races work.

    First, all racial ability score increases are flexible: you can put them into any ability score, so long as you don’t increase the same ability score more than once. This break races out of the niches which they previously filled based on their ability scores, making your other racial traits a much more interesting factor since you can always get that crucial +1 to your class’s most important ability score.

    Second, races can trade racial proficiencies for equivalent proficiencies or for less powerful ones. The allows races total flexibility for skill proficiencies, and dramatically improve flexibility for weapons and tools. Races which grant martial weapons proficiencies now essentially no longer need martial weapon proficiency from their class, and proficiency with martial weapons is a less significant advantage compared to classes limited to simple weapons.

    The ability to rearrange ability score increases and racial skill proficiencies has created a sort of “base line” for races: +2/+1 increases, Darkvision, two skills, and one or two distinguishing racial traits. Numerous races fit that mold, including races like the Kenku, the Orc, and the Tabaxi.

    Classes

    The introduction of Optional Class Features offers a lot of room to improve upon the design of the core class features of every class except the Artificer. This did a lot to address pain points in several classes, but it’s not clear how these features will be handled by the community.

    If you want to make use of optional class features, I encourage you to share my Practical Guide to Optional Class Features with your DM and your group.

    Best Of

    This section details some “best” options in major categories of character options.

    Best Race

    Undecided, and competition is fierce.

    Variant Humans were previously the best race since day one. Access to a feat at level 1 and flexible ability increases defined the meta. Previously, any time you built a character you needed to ask yourself “how is this better than a variant human?”, and in a problematically large number of cases the answer was “it isn’t”, so you were choosing a less-optimal race because it was more fun than yet another variant human.

    Thanks to Tasha’s, other races gained the ability to reassign their ability scores, and now its a competition between the benefits of one feat and one skill compared to whatever another race offers. The Custom Lineage offers access to a feat and a single +2 increase, further eating into the variant human’s standing as the best race, especially for classes like the Wizard where you only need on high ability score.

    The Mountain Dwarf stands out as another abnormally powerful race. Two flexible +2 increases mean two 16s at level 1 and possibly two 18s at level 4. That alone is tempting, and the dwarf’s core racial traits are excellent on their own.

    The Aarakocra also stands out: +2/+1 and flight is good on nearly every class, especially if you’re not forced to fight in melee. But unless you need that 50 ft. fly speed, the Winged Tiefling is a better choice, adding Darkvision, resistance to fire damage, and the ability to fly in medium armor where the Aarakocra could only fly in light armor.

    Best Class

    Undecided, but I think it’s between the Artificer and the Bard. Either one is a welcome addition to literally any party, can thrive in the full spectrum of situations common to Dungeons and Dragons, and borrows many of the most important options from other classes.

    Best Feat

    Polearm Master or Crossbow Expert. They feature centrally in numerous high-powered builds across a broad range of classes.

    Worst Of

    This section details some “worst” options in each category.

    Worst Race

    Standard Human. Bland since the Player’s Handbook hit shelves, the Standard Human has remained uninteresting and borderline unplayable through the game’s history and shows no signs of changing.

    Worst Class

    Undecided. Previously held by the Ranger, the introduction of replacement features for the Ranger and improvements to the Beast Master subclass has shifted their place in the meta, as well as making the class much more satisfying to play.

    Worst Feat

    Grappler. The feat was already bad, but errata issued early in 5e’s life removed a portion of the feat which referenced rules which didn’t make it into the final version of the game. That alone should indicate how little WotC put into this feat. Weirdly, it’s also the only feat in the SRD.

    Sours: https://rpgbot.net/dnd5/characters/state-of-the-meta/

    Edition optimization 5th

    Engineering Optimization: Theory and Practice, 5th Edition

    Preface xvii

    Acknowledgment xxi

    About the Author xxiii

    1 Introduction to Optimization 1

    1.1 Introduction 1

    1.2 Historical Development 3

    1.2.1 Modern Methods of Optimization 4

    1.3 Engineering Applications of Optimization 5

    1.4 Statement of an Optimization Problem 6

    1.4.1 Design Vector 6

    1.4.2 Design Constraints 7

    1.4.3 Constraint Surface 7

    1.4.4 Objective Function 8

    1.4.5 Objective Function Surfaces 9

    1.5 Classification of Optimization Problems 14

    1.5.1 Classification Based on the Existence of Constraints 14

    1.5.2 Classification Based on the Nature of the Design Variables 14

    1.5.3 Classification Based on the Physical Structure of the Problem 15

    1.5.4 Classification Based on the Nature of the Equations Involved 18

    1.5.5 Classification Based on the Permissible Values of the Design Variables 27

    1.5.6 Classification Based on the Deterministic Nature of the Variables 28

    1.5.7 Classification Based on the Separability of the Functions 29

    1.5.8 Classification Based on the Number of Objective Functions 31

    1.6 Optimization Techniques 33

    1.7 Engineering Optimization Literature 34

    1.8 Solutions Using MATLAB 34

    References and Bibliography 34

    Review Questions 40

    Problems 41

    2 Classical Optimization Techniques 57

    2.1 Introduction 57

    2.2 Single-Variable Optimization 57

    2.3 Multivariable Optimization with no Constraints 62

    2.3.1 Definition: rth Differential of f 62

    2.3.2 Semidefinite Case 67

    2.3.3 Saddle Point 67

    2.4 Multivariable Optimization with Equality Constraints 69

    2.4.1 Solution by Direct Substitution 69

    2.4.2 Solution by the Method of Constrained Variation 71

    2.4.3 Solution by the Method of Lagrange Multipliers 77

    2.5 Multivariable Optimization with Inequality Constraints 85

    2.5.1 Kuhn–Tucker Conditions 90

    2.5.2 Constraint Qualification 90

    2.6 Convex Programming Problem 96

    References and Bibliography 96

    Review Questions 97

    Problems 98

    3 Linear Programming I: Simplex Method 109

    3.1 Introduction 109

    3.2 Applications of Linear Programming 110

    3.3 Standard form of a Linear Programming Problem 112

    3.3.1 Scalar Form 112

    3.3.2 Matrix Form 112

    3.4 Geometry of Linear Programming Problems 114

    3.5 Definitions and Theorems 117

    3.5.1 Definitions 117

    3.5.2 Theorems 120

    3.6 Solution of a System of Linear Simultaneous Equations 122

    3.7 Pivotal Reduction of a General System of Equations 123

    3.8 Motivation of the Simplex Method 127

    3.9 Simplex Algorithm 128

    3.9.1 Identifying an Optimal Point 128

    3.9.2 Improving a Nonoptimal Basic Feasible Solution 129

    3.10 Two Phases of the Simplex Method 137

    3.11 Solutions Using MATLAB 143

    References and Bibliography 143

    Review Questions 143

    Problems 145

    4 Linear Programming II: Additional Topics and Extensions 159

    4.1 Introduction 159

    4.2 Revised Simplex Method 159

    4.3 Duality in Linear Programming 173

    4.3.1 Symmetric Primal–Dual Relations 173

    4.3.2 General Primal–Dual Relations 174

    4.3.3 Primal–Dual Relations when the Primal Is in Standard Form 175

    4.3.4 Duality Theorems 176

    4.3.5 Dual Simplex Method 176

    4.4 Decomposition Principle 180

    4.5 Sensitivity or Postoptimality Analysis 187

    4.5.1 Changes in the Right-Hand-Side Constants bi 188

    4.5.2 Changes in the Cost Coefficients cj 192

    4.5.3 Addition of New Variables 194

    4.5.4 Changes in the Constraint Coefficients aij 195

    4.5.5 Addition of Constraints 197

    4.6 Transportation Problem 199

    4.7 Karmarkar’s Interior Method 202

    4.7.1 Statement of the Problem 203

    4.7.2 Conversion of an LP Problem into the Required Form 203

    4.7.3 Algorithm 205

    4.8 Quadratic Programming 208

    4.9 Solutions Using Matlab 214

    References and Bibliography 214

    Review Questions 215

    Problems 216

    5 Nonlinear Programming I: One-Dimensional Minimization Methods 225

    5.1 Introduction 225

    5.2 Unimodal Function 230

    Elimination Methods 231

    5.3 Unrestricted Search 231

    5.3.1 Search with Fixed Step Size 231

    5.3.2 Search with Accelerated Step Size 232

    5.4 Exhaustive Search 232

    5.5 Dichotomous Search 234

    5.6 Interval Halving Method 236

    5.7 Fibonacci Method 238

    5.8 Golden Section Method 243

    5.9 Comparison of Elimination Methods 246

    Interpolation Methods 247

    5.10 Quadratic Interpolation Method 248

    5.11 Cubic Interpolation Method 253

    5.12 Direct Root Methods 259

    5.12.1 Newton Method 259

    5.12.2 Quasi-Newton Method 261

    5.12.3 Secant Method 263

    5.13 Practical Considerations 265

    5.13.1 How to Make the Methods Efficient and More Reliable 265

    5.13.2 Implementation in Multivariable Optimization Problems 266

    5.13.3 Comparison of Methods 266

    5.14 Solutions Using MATLAB 267

    References and Bibliography 267

    Review Questions 267

    Problems 268

    6 Nonlinear Programming II: Unconstrained Optimization Techniques 273

    6.1 Introduction 273

    6.1.1 Classification of Unconstrained Minimization Methods 276

    6.1.2 General Approach 276

    6.1.3 Rate of Convergence 276

    6.1.4 Scaling of Design Variables 277

    Direct Search Methods 280

    6.2 Random Search Methods 280

    6.2.1 Random Jumping Method 280

    6.2.2 Random Walk Method 282

    6.2.3 Random Walk Method with Direction Exploitation 283

    6.2.4 Advantages of Random Search Methods 284

    6.3 Grid Search Method 285

    6.4 Univariate Method 285

    6.5 Pattern Directions 288

    6.6 Powell’s Method 289

    6.6.1 Conjugate Directions 289

    6.6.2 Algorithm 293

    6.7 Simplex Method 298

    6.7.1 Reflection 298

    6.7.2 Expansion 301

    6.7.3 Contraction 301

    Indirect Search (Descent) Methods 304

    6.8 Gradient of a Function 304

    6.8.1 Evaluation of the Gradient 306

    6.8.2 Rate of Change of a Function Along a Direction 307

    6.9 Steepest Descent (Cauchy) Method 308

    6.10 Conjugate Gradient (Fletcher–Reeves) Method 310

    6.10.1 Development of the Fletcher–Reeves Method 310

    6.10.2 Fletcher–Reeves Method 311

    6.11 Newton’s Method 313

    6.12 Marquardt Method 316

    6.13 Quasi-Newton Methods 317

    6.13.1 Computation of [Bi] 318

    6.13.2 Rank 1 Updates 319

    6.13.3 Rank 2 Updates 320

    6.14 Davidon–Fletcher–Powell Method 321

    6.15 Broyden–Fletcher–Goldfarb–Shanno Method 327

    6.16 Test Functions 330

    6.17 Solutions Using Matlab 332

    References and Bibliography 333

    Review Questions 334

    Problems 336

    7 Nonlinear Programming III: Constrained Optimization Techniques 347

    7.1 Introduction 347

    7.2 Characteristics of a Constrained Problem 347

    Direct Methods 350

    7.3 Random Search Methods 350

    7.4 Complex Method 351

    7.5 Sequential Linear Programming 353

    7.6 Basic Approach in the Methods of Feasible Directions 360

    7.7 Zoutendijk’s Method of Feasible Directions 360

    7.7.1 Direction-Finding Problem 362

    7.7.2 Determination of Step Length 364

    7.7.3 Termination Criteria 367

    7.8 Rosen’s Gradient Projection Method 369

    7.8.1 Determination of Step Length 372

    7.9 Generalized Reduced Gradient Method 377

    7.10 Sequential Quadratic Programming 386

    7.10.1 Derivation 386

    7.10.2 Solution Procedure 389

    Indirect Methods 392

    7.11 Transformation Techniques 392

    7.12 Basic Approach of the Penalty Function Method 394

    7.13 Interior Penalty Function Method 396

    7.14 Convex Programming Problem 405

    7.15 Exterior Penalty Function Method 406

    7.16 Extrapolation Techniques in the Interior Penalty Function Method 410

    7.16.1 Extrapolation of the Design Vector X 410

    7.16.2 Extrapolation of the Function f 412

    7.17 Extended Interior Penalty Function Methods 414

    7.17.1 Linear Extended Penalty Function Method 414

    7.17.2 Quadratic Extended Penalty Function Method 415

    7.18 Penalty Function Method for Problems with Mixed Equality and Inequality Constraints 416

    7.18.1 Interior Penalty Function Method 416

    7.18.2 Exterior Penalty Function Method 418

    7.19 Penalty Function Method for Parametric Constraints 418

    7.19.1 Parametric Constraint 418

    7.19.2 Handling Parametric Constraints 420

    7.20 Augmented Lagrange Multiplier Method 422

    7.20.1 Equality-Constrained Problems 422

    7.20.2 Inequality-Constrained Problems 423

    7.20.3 Mixed Equality–Inequality-Constrained Problems 425

    7.21 Checking the Convergence of Constrained Optimization Problems 426

    7.21.1 Perturbing the Design Vector 427

    7.21.2 Testing the Kuhn–Tucker Conditions 427

    7.22 Test Problems 428

    7.22.1 Design of a Three-Bar Truss 429

    7.22.2 Design of a Twenty-Five-Bar Space Truss 430

    7.22.3 Welded Beam Design 431

    7.22.4 Speed Reducer (Gear Train) Design 433

    7.22.5 Heat Exchanger Design [7.42] 435

    7.23 Solutions Using MATLAB 435

    References and Bibliography 435

    Review Questions 437

    Problems 439

    8 Geometric Programming 449

    8.1 Introduction 449

    8.2 Posynomial 449

    8.3 Unconstrained Minimization Problem 450

    8.4 Solution of an Unconstrained Geometric Programming Program using Differential Calculus 450

    8.4.1 Degree of Difficulty 453

    8.4.2 Sufficiency Condition 453

    8.4.3 Finding the Optimal Values of Design Variables 453

    8.5 Solution of an Unconstrained Geometric Programming Problem Using Arithmetic–Geometric Inequality 457

    8.6 Primal–dual Relationship and Sufficiency Conditions in the Unconstrained Case 458

    8.6.1 Primal and Dual Problems 461

    8.6.2 Computational Procedure 461

    8.7 Constrained Minimization 464

    8.8 Solution of a Constrained Geometric Programming Problem 465

    8.8.1 Optimum Design Variables 466

    8.9 Primal and Dual Programs in the Case of Less-than Inequalities 466

    8.10 Geometric Programming with Mixed Inequality Constraints 473

    8.11 Complementary Geometric Programming 475

    8.11.1 Solution Procedure 477

    8.11.2 Degree of Difficulty 478

    8.12 Applications of Geometric Programming 480

    References and Bibliography 491

    Review Questions 493

    Problems 493

    9 Dynamic Programming 497

    9.1 Introduction 497

    9.2 Multistage Decision Processes 498

    9.2.1 Definition and Examples 498

    9.2.2 Representation of a Multistage Decision Process 499

    9.2.3 Conversion of a Nonserial System to a Serial System 500

    9.2.4 Types of Multistage Decision Problems 501

    9.3 Concept of Suboptimization and Principle of Optimality 501

    9.4 Computational Procedure in Dynamic Programming 505

    9.5 Example Illustrating the Calculus Method of Solution 507

    9.6 Example Illustrating the Tabular Method of Solution 512

    9.6.1 Suboptimization of Stage 1 (Component 1) 514

    9.6.2 Suboptimization of Stages 2 and 1 (Components 2 and 1) 514

    9.6.3 Suboptimization of Stages 3, 2, and 1 (Components 3, 2, and 1) 515

    9.7 Conversion of a Final Value Problem into an Initial Value Problem 517

    9.8 Linear Programming as a Case of Dynamic Programming 519

    9.9 Continuous Dynamic Programming 523

    9.10 Additional Applications 526

    9.10.1 Design of Continuous Beams 526

    9.10.2 Optimal Layout (Geometry) of a Truss 527

    9.10.3 Optimal Design of a Gear Train 528

    9.10.4 Design of a Minimum-Cost Drainage System 529

    References and Bibliography 530

    Review Questions 531

    Problems 532

    10 Integer Programming 537

    10.1 Introduction 537

    Integer Linear Programming 538

    10.2 Graphical Representation 538

    10.3 Gomory’s Cutting Plane Method 540

    10.3.1 Concept of a Cutting Plane 540

    10.3.2 Gomory’s Method for All-Integer Programming Problems 541

    10.3.3 Gomory’s Method for Mixed-Integer Programming Problems 547

    10.4 Balas’ Algorithm for Zero–One Programming Problems 551

    Integer Nonlinear Programming 553

    10.5 Integer Polynomial Programming 553

    10.5.1 Representation of an Integer Variable by an Equivalent System of Binary Variables 553

    10.5.2 Conversion of a Zero–One Polynomial Programming Problem into a Zero–One LP Problem 555

    10.6 Branch-and-Bound Method 556

    10.7 Sequential Linear Discrete Programming 561

    10.8 Generalized Penalty Function Method 564

    10.9 Solutions Using MATLAB 569

    References and Bibliography 569

    Review Questions 570

    Problems 571

    11 Stochastic Programming 575

    11.1 Introduction 575

    11.2 Basic Concepts of Probability Theory 575

    11.2.1 Definition of Probability 575

    11.2.2 Random Variables and Probability Density Functions 576

    11.2.3 Mean and Standard Deviation 578

    11.2.4 Function of a Random Variable 580

    11.2.5 Jointly Distributed Random Variables 581

    11.2.6 Covariance and Correlation 583

    11.2.7 Functions of Several Random Variables 583

    11.2.8 Probability Distributions 585

    11.2.9 Central Limit Theorem 589

    11.3 Stochastic Linear Programming 589

    11.4 Stochastic Nonlinear Programming 594

    11.4.1 Objective Function 594

    11.4.2 Constraints 595

    11.5 Stochastic Geometric Programming 600

    References and Bibliography 602

    Review Questions 603

    Problems 604

    12 Optimal Control and Optimality Criteria Methods 609

    12.1 Introduction 609

    12.2 Calculus of Variations 609

    12.2.1 Introduction 609

    12.2.2 Problem of Calculus of Variations 610

    12.2.3 Lagrange Multipliers and Constraints 615

    12.2.4 Generalization 618

    12.3 Optimal Control Theory 619

    12.3.1 Necessary Conditions for Optimal Control 619

    12.3.2 Necessary Conditions for a General Problem 621

    12.4 Optimality Criteria Methods 622

    12.4.1 Optimality Criteria with a Single Displacement Constraint 623

    12.4.2 Optimality Criteria with Multiple Displacement Constraints 624

    12.4.3 Reciprocal Approximations 625

    References and Bibliography 628

    Review Questions 628

    Problems 629

    13 Modern Methods of Optimization 633

    13.1 Introduction 633

    13.2 Genetic Algorithms 633

    13.2.1 Introduction 633

    13.2.2 Representation of Design Variables 634

    13.2.3 Representation of Objective Function and Constraints 635

    13.2.4 Genetic Operators 636

    13.2.5 Algorithm 640

    13.2.6 Numerical Results 641

    13.3 Simulated Annealing 641

    13.3.1 Introduction 641

    13.3.2 Procedure 642

    13.3.3 Algorithm 643

    13.3.4 Features of the Method 644

    13.3.5 Numerical Results 644

    13.4 Particle Swarm Optimization 647

    13.4.1 Introduction 647

    13.4.2 Computational Implementation of PSO 648

    13.4.3 Improvement to the Particle Swarm Optimization Method 649

    13.4.4 Solution of the Constrained Optimization Problem 649

    13.5 Ant Colony Optimization 652

    13.5.1 Basic Concept 652

    13.5.2 Ant Searching Behavior 653

    13.5.3 Path Retracing and Pheromone Updating 654

    13.5.4 Pheromone Trail Evaporation 654

    13.5.5 Algorithm 655

    13.6 Optimization of Fuzzy Systems 660

    13.6.1 Fuzzy Set Theory 660

    13.6.2 Optimization of Fuzzy Systems 662

    13.6.3 Computational Procedure 663

    13.6.4 Numerical Results 664

    13.7 Neural-Network-Based Optimization 665

    References and Bibliography 667

    Review Questions 669

    Problems 671

    14 Metaheuristic Optimization Methods 673

    14.1 Definitions 673

    14.2 Metaphors Associated with Metaheuristic Optimization Methods 673

    14.3 Details of Representative Metaheuristic Algorithms 680

    14.3.1 Crow Search Algorithm 680

    14.3.2 Firefly Optimization Algorithm (FA) 681

    14.3.3 Harmony Search Algorithm 684

    14.3.4 Teaching-Learning-Based Optimization (TLBO) 687

    14.3.5 Honey Bee Swarm Optimization Algorithm 689

    References and Bibliography 692

    Review Questions 694

    15 Practical Aspects of Optimization 697

    15.1 Introduction 697

    15.2 Reduction of Size of an Optimization Problem 697

    15.2.1 Reduced Basis Technique 697

    15.2.2 Design Variable Linking Technique 698

    15.3 Fast Reanalysis Techniques 700

    15.3.1 Incremental Response Approach 700

    15.3.2 Basis Vector Approach 704

    15.4 Derivatives of Static Displacements and Stresses 705

    15.5 Derivatives of Eigenvalues and Eigenvectors 707

    15.5.1 Derivatives of ��i 707

    15.5.2 Derivatives of Yi 708

    15.6 Derivatives of Transient Response 709

    15.7 Sensitivity of Optimum Solution to Problem Parameters 712

    15.7.1 Sensitivity Equations Using Kuhn–Tucker Conditions 712

    15.7.2 Sensitivity Equations Using the Concept of Feasible Direction 714

    References and Bibliography 715

    Review Questions 716

    Problems 716

    16 Multilevel and Multiobjective Optimization 721

    16.1 Introduction 721

    16.2 Multilevel Optimization 721

    16.2.1 Basic Idea 721

    16.2.2 Method 722

    16.3 Parallel Processing 726

    16.4 Multiobjective Optimization 729

    16.4.1 Utility Function Method 730

    16.4.2 Inverted Utility Function Method 730

    16.4.3 Global Criterion Method 730

    16.4.4 Bounded Objective Function Method 730

    16.4.5 Lexicographic Method 731

    16.4.6 Goal Programming Method 732

    16.4.7 Goal Attainment Method 732

    16.4.8 Game Theory Approach 733

    16.5 Solutions Using MATLAB 735

    References and Bibliography 735

    Review Questions 736

    Problems 737

    17 Solution of Optimization Problems Using MATLAB 739

    17.1 Introduction 739

    17.2 Solution of General Nonlinear Programming Problems 740

    17.3 Solution of Linear Programming Problems 742

    17.4 Solution of LP Problems Using Interior Point Method 743

    17.5 Solution of Quadratic Programming Problems 745

    17.6 Solution of One-Dimensional Minimization Problems 746

    17.7 Solution of Unconstrained Optimization Problems 746

    17.8 Solution of Constrained Optimization Problems 747

    17.9 Solution of Binary Programming Problems 750

    17.10 Solution of Multiobjective Problems 751

    References and Bibliography 755

    Problems 755

    A Convex and Concave Functions 761

    B Some Computational Aspects of Optimization 767

    B.1 Choice of Method 767

    B.2 Comparison of Unconstrained Methods 767

    B.3 Comparison of Constrained Methods 768

    B.4 Availability of Computer Programs 769

    B.5 Scaling of Design Variables and Constraints 770

    B.6 Computer Programs for Modern Methods of Optimization 771

    References and Bibliography 772

    C Introduction to MATLAB® 773

    C.1 Features and Special Characters 773

    C.2 Defining Matrices in MATLAB 774

    C.3 Creating m-Files 775

    C.4 Optimization Toolbox 775

    Answers to Selected Problems 777

    Index 787

    Sours: https://www.wiley.com/en-us/Engineering+Optimization%3A+Theory+and+Practice%2C+5th+Edition-p-9781119454793
    The Support Lore Bard - D\u0026D: Optimized #15

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    Now discussing:

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