Engineering Optimization: Theory and Practice, Fourth Edition

7.20 Augmented Lagrange Multiplier Method 463 7.20.3 Mixed Equality–Inequality-Constrained Problems Consider the following gener ...

464 Nonlinear Programming III: Constrained Optimization Techniques Table 7.6 Results for Example 7.12 λ(i) rk x 1 ∗(i) x∗ 2 (i) ...

7.21 Checking the Convergence of Constrained Optimization Problems 465 iterative process and using the solution with confidence. ...

466 Nonlinear Programming III: Constrained Optimization Techniques test for the satisfaction of these conditions before taking a ...

7.22 Test Problems 467 7.22 Test Problems As discussed in previous sections, a number of algorithms are available for solving a ...

468 Nonlinear Programming III: Constrained Optimization Techniques whereσiis the stress induced in memberi,σ(u)the maximum permi ...

7.22 Test Problems 469 Figure 7.22 A 25-bar space truss [7.38]. =sum of deflections of nodes 1 and 2 f 3 ( X)=−ω 1 = egative of ...

470 Nonlinear Programming III: Constrained Optimization Techniques Constraints: |σij( X)|≤σmax, i= 1 , 2 ,... , 25 , j= 1 , 2 σi ...

7.22 Test Problems 471 l L h P h b t Figure 7.23 Welded beam [7.39]. Objective function:f (X)= 1. 10471 x 12 x 2 + 0. 04811 x 3 ...

472 Nonlinear Programming III: Constrained Optimization Techniques J= 2 { x 1 x 2 √ 2 [ x 22 12 + ( x 1 +x 3 2 ) 2 ]} σ(X)= 6 P ...

7.22 Test Problems 473 Objective(minimization of weight of speed reducer): f (X)= 0. 7854 x 1 x 22 ( 3333. 3 x 32 + 41. 9334 x 3 ...

474 Nonlinear Programming III: Constrained Optimization Techniques Constraints: g 1 ( X)= 0. 0025 (x 4 +x 6 )− 1 ≤ 0 g 2 (X)= 0. ...

7.23 MATLAB Solution of Constrained Optimization Problems 475 Step 3: Invoke constrained optimization program (write this in new ...

476 Nonlinear Programming III: Constrained Optimization Techniques -0.0000 -0.0000 -3.5858 0 -1.4142 -1.4142 ceq = [] References ...

References and Bibliography 477 7.18 D. Kavlie and J. Moe, Automated design of frame structure,ASCE Journal of the Struc- tural ...

478 Nonlinear Programming III: Constrained Optimization Techniques 7.39 K. M. Ragsdell and D. T. Phillips, Optimal design of a c ...

Review Questions 479 (h)The solutions of all LP problems in the SLP method lie in the infeasible domain of the original problem. ...

480 Nonlinear Programming III: Constrained Optimization Techniques 7.21 Construct theφkfunction to be used for a mixed equality– ...

Problems 481 7.4 Consider the tubular column described in Example 1.1. Starting from the design vector (d= 8 .0 cm,t= 0 .4 cm), ...

482 Nonlinear Programming III: Constrained Optimization Techniques 7.9 Minimizef (X)= 9 x 12 + 6 x 22 +x^23 − 18 x 1 − 12 x 2 − ...