Engineering Optimization: Theory and Practice, Fourth Edition

366 Nonlinear Programming II: Unconstrained Optimization Techniques

SOLUTION

Step 1: Write an M-fileobjfun.m for the objective function.

function f= objfun (x)

f= 100* (x(2)-x(1) *x(1))^2+(1-x(1))^2;

Step 2: Invoke unconstrained optimization program (write this in new MATLAB file).

clc

clear all

warning off

x0 = [-1.2,1.0]; % Starting guess

fprintf ('The values of function value at starting

pointn');

f=objfun(x0)

options = optimset('LargeScale', 'off');

[x, fval] = fminunc (@objfun,x0,options)

This produces the solution or ouput as follows:

The values of function value at starting point

f=

24.2000

Optimization terminated: relative infinity-norm of gradi-

ent less than options.TolFun.

x=

1.0000 1.0000

fval=

2.8336e-011

References and Bibliography

6.1 S. S. Rao,The Finite Element Method in Engineering, 4th ed., Elsevier Butterworth

Heinemann, Burlington, MA, 2005.

6.2 T. F. Edgar and D. M. Himmelblau,Optimization of Chemical Processes, McGraw-Hill,

New York, 1988.

6.3 R. L. Fox,Optimization Methods for Engineering Design, Addison-Wesley, Reading, MA,

1971.

6.4 W. E. Biles and J. J. Swain,Optimization and Industrial Experimentation, Wiley, New

York, 1980.

6.5 C. R. Hicks,Fundamental Concepts in the Design of Experiments, Saunders College

Publishing, Fort Worth, TX, 1993.

6.6 R. Hooke and T. A. Jeeves, Direct search solution of numerical and statistical problems,

Journal of the ACM, Vol. 8, No. 2, pp. 212–229, 1961.

6.7 M.J.D. Powell, An efficient method for finding the minimum of a function of several

variables without calculating derivatives,Computer Journal, Vol. 7, No. 4, pp. 303–307,

1964.