Engineering Optimization: Theory and Practice, Fourth Edition

6.16 Test Functions 363 Iteration 2 (i= 2 ) The next search direction is determined as S 2 = −[B 2 ]∇f 2 = − [ 1 2 − 1 2 −^1252 ...

364 Nonlinear Programming II: Unconstrained Optimization Techniques 2.A quadratic function: f (x 1 , x 2 ) =(x 1 + 2 x 2 − 7 )^2 ...

6.17 MATLAB Solution of Unconstrained Optimization Problems 365 X 1 = { 0. 5 − 2 } , X∗= { 5 4 } , X∗alternate= { 11. 41... − 0. ...

366 Nonlinear Programming II: Unconstrained Optimization Techniques SOLUTION Step 1: Write an M-fileobjfun.m for the objective f ...

References and Bibliography 367 6.8 H. H. Rosenbrock, An automatic method for finding the greatest or least value of a function, ...

368 Nonlinear Programming II: Unconstrained Optimization Techniques 6.30 A. R. Colville,A Comparative Study of Nonlinear Program ...

Review Questions 369 6.16 Why is Powell’s method called a pattern search method? 6.17 What are the roles of univariate and patte ...

370 Nonlinear Programming II: Unconstrained Optimization Techniques Problems 6.1 A bar is subjected to an axial load,P 0 , as sh ...

Problems 371 Figure 6.18 Tapered cantilever beam. Figure 6.19 Three-degree-of-freedom spring–mass system. 6.4 The steady-state t ...

372 Nonlinear Programming II: Unconstrained Optimization Techniques Figure 6.20 Straight fin. 6.5 Figure 6.21 shows two bodies,A ...

Problems 373 q Figure 6.22 Two-bar truss. (b)Find the steepest descent direction,S 1 , offat the trial vectorX 1 = { 0 0 } . (c) ...

374 Nonlinear Programming II: Unconstrained Optimization Techniques Figure 6.23 Three carts interconnected by springs. 6.9 Plot ...

Problems 375 6.15 Find a suitable transformation or scaling of variables to reduce the condition number of the Hessian matrix of ...

376 Nonlinear Programming II: Unconstrained Optimization Techniques 6.27 Perform two iterations of the Marquardt’s method to min ...

Problems 377 6.35 Consider the minimization of the function f= 1 x 12 +x 22 + 2 Perform one iteration of Newton’s method from th ...

378 Nonlinear Programming II: Unconstrained Optimization Techniques 6.45 Minimizef= 4 x 12 + 3 x^22 − 5 x 1 x 2 − 8 x 1 starting ...

Problems 379 6.54 Same as Problem 6.53 for the following function: f=(x 2 −x 12 )^2 +( 1 −x 1 )^2 6.55 Verify whether the follow ...

7 Nonlinear Programming III: Constrained Optimization Techniques 7.1 Introduction This chapter deals with techniques that are ap ...

7.2 Characteristics of a Constrained Problem 381 Table 7.1 Constrained Optimization Techniques Direct methods Indirect methods R ...

382 Nonlinear Programming III: Constrained Optimization Techniques Figure 7.2 Constrained minimum occurring on a nonlinear const ...