Engineering Optimization: Theory and Practice, Fourth Edition

38 Introduction to Optimization

SOLUTION

Step 1: Write an M-fileprobofminobj.mfor the objective function.

function f= probofminobj (x)

f= 9.82*x(1)*x(2)+2*x(1);

Step 2: Write an M-fileconprobformin.mfor the constraints.

function [c, ceq] = conprobformin(x)

% Nonlinear inequality constraints

c = [2500/(pi*x(1)*x(2))-500;2500/(pi*x(1)*x(2))-

(pi^2*(x(1)^2+x(2)^2))/0.5882;-x(1)+2;x(1)-14;-x(2)+0.2;

x(2)-0.8];

% Nonlinear equality constraints

ceq = [];

Step 3: Invoke constrained optimization program (write this in new matlab file).

clc

clear all

warning off

x0 = [7 0.4]; % Starting guess\

fprintf ('The values of function value and constraints

at starting point\n');

f=probofminobj (x0)

[c, ceq] = conprobformin (x0)

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

[x, fval]=fmincon (@probofminobj, x0, [], [], [], [], [],

[], @conprobformin, options)

fprintf('The values of constraints at optimum solution\n');

[c, ceq] = conprobformin(x) % Check the constraint values at x

This produces the solution or output as follows:

The values of function value and constraints at starting point

f=

41.4960

c =

-215.7947

-540.6668

-5.0000

-7.0000

-0.2000

-0.4000

ceq =

[]

Optimization terminated: first-order optimality

measure less