Engineering Optimization: Theory and Practice, Fourth Edition

474 Nonlinear Programming III: Constrained Optimization Techniques

Constraints:

g 1 ( X)= 0. 0025 (x 4 +x 6 )− 1 ≤ 0

g 2 (X)= 0. 0025 (−x 4 +x 5 +x 7 )− 1 ≤ 0

g 3 (X)= 0. 01 (−x 5 +x 8 )− 1 ≤ 0

g 4 ( X)= 100 x 1 −x 1 x 6 + 338. 33252 x 4 − 38 , 333. 333 ≤ 0

g 5 (X)=x 2 x 4 −x 2 x 7 − 2501 x 4 + 2501 x 5 ≤ 0

g 6 (X)=x 3 x 5 −x 3 x 8 − 5002 x 5 + 1 , 250 , 000 ≤ 0

g 7 : 100≤x 1 ≤ 01 ,000 :g 8

g 9 : 1000≤x 2 ≤ 01 ,000 :g 10

g 11 : 1000≤x 3 ≤ 01 ,000 :g 12

g 13 tog 22 : 10≤xi≤ 0001 , i= 4 , 5 ,... , 8

Optimum solution: X∗= { 67 1357 5125 181 295 219 286 395 5 }T,

f∗= 0497

7.23 MATLAB Solution of Constrained Optimization Problems

The solution of multivariable minimization problems, with inequality and equality con-

straints, using the MATLAB functionfminconis illustrated in this section.

Example 7.13 Find the solution of Example 7.8 starting from the initial point

X 1 = { 0. 1 0 .1 3. 0 }T

SOLUTION

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

function f= objfun (x)

f= x(1)^3-6*x(1)^2+11*x(1)+x(3);

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

function [c, ceq] = constraints (x)

% Nonlinear inequality constraints

c = [x(1)^2+x(2)^2-x(3)^2;4-x(1)^2-x(2)^2-x(3)^2;x(3)-5;

• -x(1);-x(2);-x(3)];
  % Nonlinear equality constraints
  ceq = [];