Introduction to Optimum Design phần 9 ppsx

... x uii i =+- () [] =25 50 0 01 1 99 23 ln . ; to f i x ux ii x x () =- + - - () Ê Ë ˆ ¯ 100 1 1 2 3 exp ff i i xx () = () = Â 2 1 99 xx 12 0, ≥ 1 2 1 5 10 0 12 xx+-£. 590 INTRODUCTION TO OPTIMUM DESIGN ... Optimum Design 591 18.6 (Hock and Schittkowski, 198 1) minimize subject to 18.7 (Hock and Schittkowski, 198 1) minimize subject to 18.8 (Hock and Schittkowski, 198 1)...

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... 0, 0). 9. 16 x (1) = (-2.7068, 0.88168). 9. 17 x (1) = (3.771567, 0.3355 89) . 9. 18 x (1) = (4 .99 913, 24 .99 085). 9. 19 x (1) = (-1.268 59, -0.7 597 3, 0.73141, 0. 398 33). 9. 22 x (2) = (4, 2). 9. 23 x (2) = ... 2.2835mm. 9. 45 x 1 = 2.2213mm, x 2 = 1. 897 8mm. 9. 46 x* = 0.6 190 84. 9. 47 x* = 9. 424753. 9. 48 x* = 1.570807. 9. 49 x* = 1. 496 045. 9. 50 x* = (3.667328, 0....

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... America 0405060708 09 987654321 Table of Contents Preface ix Chapter 1 Introduction to Design 1 1.1 The Design Process 2 1.2 Engineering Design versus Engineering Analysis 4 1.3 Conventional versus Optimum Design ... Gradient Vector 310 9. 2.2 Orthogonality of Steepest Descent Directions 314 9. 3 Scaling of Design Variables 315 9. 4 Search Direction Determination: Newton’s...

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... of a design problem may not be linear, in which case curves must be plotted to identify the feasible region, and contours or iso-cost curves must be drawn to identify the optimum design. To plot ... concepts related to optimum design problems. In the following section, a design optimization problem is formulated and used to describe the solution process. Some concepts rel...

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... m i i j j x0,0 x0,0* * ; * * ;1 1to and to 144 INTRODUCTION TO OPTIMUM DESIGN 4.51 Consider the following problem with equality constraints: Minimize (x 1 - 1) 2 + (x 2 - 1) 2 subject to x 1 + x 2 - 4 = 0 x 1 - ... of its use. 176 INTRODUCTION TO OPTIMUM DESIGN TABLE 5-1 Alternate Form of KKT Necessary Conditions Problem: minimize f(x) subject to h i (x) = 0, i = 1 to...

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... 0 6.67 Maximize z = x 1 + 4x 2 subject to x 1 + 2x 2 £ 5 2x 1 + x 2 = 4 254 INTRODUCTION TO OPTIMUM DESIGN 232 INTRODUCTION TO OPTIMUM DESIGN 1. For 2x 1 + x 2 £ 9: y 1 = 1.6 (c¢ 3 in column x 3 ) 2. ... 18x 2 subject to x 1 - 3x 2 £-3 2x 1 + 2x 2 ≥ 5 x 1 , x 2 ≥ 0 6.11 Minimize f = 20x 1 - 6x 2 subject to 3x 1 - x 2 ≥ 3 Linear Programming Methods for Optimum Design...

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... positive. 300 INTRODUCTION TO OPTIMUM DESIGN 322 INTRODUCTION TO OPTIMUM DESIGN FIGURE 9- 7 Iteration history for Example 9. 7 with Newton’s method. TABLE 9- 2 Optimum Solution for Example 9. 7 with Modified ... applications. TABLE 9- 3 Evaluation of Three Methods for Example 9. 8: f(x) = 50(x 2 - x 2 1 ) 2 + (2 - x 1 ) 2 Steepest descent Conjugate gradient Modified Newt...

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... Exercise 2.14 at the point P 1 = 2 and P 2 = 1. 376 INTRODUCTION TO OPTIMUM DESIGN

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... 2.27873E+01 7.87500E+02 9. 9438E+00 9. 9438E+00 1.0000E-01 3 1.25020E-02 1.3 199 3E+00 7.13063E+02 9. 0133E+00 9. 0133E+00 1.0000E-01 4 2. 199 48E-02 1.03643E-01 6 .99 734E+02 7. 693 3E+00 1.0000E+01 1.0000E-01 5 ... 9. 0828E+00 9 CCC 4.2 495 0E-04 1.67623E-02 1.27 298 E-02 5.3485E-02 4.0151E-01 9. 0831E+00 10 CCS 1.0 895 7E-04 1.67623E-02 1.27 290 E-02 5.3 395 E-02 3 .99 16E-01 9. 1...

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... references cited there (Arora et al., 199 4; Arora and Huang, 199 6; Huang and Arora, 199 5, 199 7a,b; Huang et al., 199 7; Arora, 199 7, 2002; Kocer and Arora 199 6a,b, 199 7, 199 9, 2002). These references contain ... 16100 895 15.00 1010 123 3.750 W36 ¥ 230 67.60 35 .90 0.760 16.470 1.260 15000 837 14 .90 94 0 114 3.730 W36 ¥ 210 61.80 36. 69 0.830 12.180 1.360 13200 7 19 14.60 411 67...

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