Review Questions 295
This produces the solution or ouput as follows:
x=
0.4809
fval =
-0.3100
References and Bibliography
5.1 J. S. Przemieniecki,Theory of Matrix Structural Analysis, McGraw-Hill, New York, 1968.
5.2 M. J. D. Powell, An efficient method for finding the minimum of a function of sev-
eral variables without calculating derivatives,Computer Journal, Vol. 7, pp. 155–162,
1964.
5.3 R. Fletcher and C. M. Reeves, Function minimization by conjugate gradients,Computer
Journal, Vol. 7, pp. 149–154, 1964.
5.4 B. Carnahan, H. A. Luther, and J. O. Wilkes,Applied Numerical Methods, Wiley, New
York, 1969.
5.5 R. L. Fox,Optimization Methods for Engineering Design, Addison-Wesley, Reading, MA,
1971.
5.6 D. J. Wilde,Optimum Seeking Methods, Prentice Hall, Englewood Cliffs, NJ, 1964.
5.7 A. I. Cohen, Stepsize analysis for descent methods,Journal of Optimization Theory and
Applications, Vol. 33, pp. 187–205, 1981.
5.8 P. E. Gill, W. Murray, and M. H. Wright,Practical Optimization, Academic Press, New
York, 1981.
5.9 J. E. Dennis and R. B. Schnabel,Numerical Methods for Unconstrained Optimization and
Nonlinear Equations, Prentice Hall, Englewood Cliffs, NJ, 1983.
5.10 R. P. Brent,Algorithms for Minimization Without Derivatives, Prentice Hall, Englewood
Cliffs, NJ, 1973.
5.11 W. C. Davidon, Variable metric method for minimization, Argonne National Laboratory,
ANL-5990 (rev), 1959.
Review Questions
5.1 What is a one-dimensional minimization problem?
5.2 What are the limitations of classical methods in solving a one-dimensional minimization
problem?
5.3 What is the difference between elimination and interpolation methods?
5.4 Define Fibonacci numbers.
5.5 What is the difference between Fibonacci and golden section methods?
5.6 What is a unimodal function?
5.7 What is an interval of uncertainty?
5.8 Suggest a method of finding the minimum of a multimodal function.
5.9 What is an exhaustive search method?
