Page 331 - MATLAB an introduction with applications

316 ——— MATLAB: An Introduction with Applications

REFERENCES

1. Arora, J.S., Introduction to Optimum Design, McGraw-Hill, New York, 1989.
2. Papalambros, P.Y. and Wilde, D.J., Principles of Optimal Design, Cambridge University Press,
Cambridge, 1988.
3. Siddall, J.N., Optimal Engineering Design: Principles and Applications, Marcel Dekker, New York,
1982.
nd
4. Rao, S.S., Optimization: Theory and Applications, 2 ed., Wiley, New York, 1984.
5. Vanderplatts, G .N., Numerical Optimization Techniques for Engineering Design with Applications,
McGraw-Hill, New York, 1984.
6. Fox, R.L., Optimization Methods for Engineering Design, Addison-Wesley, Reading, MA, 1972.
7. Recklaitis, G.V., Ravindran, A. and Ragsdell, K.M., Engineering Optimization: Methods and
Applications, Wiley, New York, 1983.
8. Shoup, T.E. and Mistree, F., Optimization Methods with Applications for Personal Computers, Prentice-
Hall, Englewood Cliffs, NJ, 1987.

PROBLEMS

2
2
P5.1: Minimize f(x , x ) = x – 0.5x + 2x + 2x x + x using Newton’s method. Starting point: (0, 0).
1
1
1 2
2
2
2
1
8
2
P5.2: Use Newton’s method to find the maximum of f(x) = 5 sin x – x with the initial guess of x = 1, 8.
19 0
P5.3: Fit a polynomial by quadratic approximation and find the value of x at which F(x) is minimum.
x F () x
1 12
2 7
3 20
P5.4: Fit a polynomial by quadratic approximation and find the value of x at which F(x) is minimum.
x F () x
1 20
2 –17
3 15

P5.5: Find the minimum of the following function using Powell’s method:
2
() =
2
Fx 4x + 3x − 5x x − 8x 1
1 2
2
1
Starting from (0, 0).