Problems 485subject to
0 ≤x 10 ≤x 2 ≤x 1
√
3
0 ≤x 1 +√
3 x 2 ≤ 67.23 Construct theφkfunction, according to(a)interior and(b)exterior penalty function
methods and plot its contours for the following problem:
Maximizef= 2 xsubject to
2 ≤x≤ 107.24 Construct theφkfunction according to the exterior penalty function approach and complete
the minimization ofφkfor the following problem.
Minimizef (x)=(x− 1 )^2subject to
g 1 (x)= 2 −x≤ 0 , g 2 (x)=x− 4 ≤ 07.25 Plot the contours of theφkfunction using the quadratic extended interior penalty function
method for the following problem:
Minimizef (x)=(x− 1 )^2subject to
g 1 (x)= 2 −x≤ 0 , g 2 (x)=x− 4 ≤ 07.26 Consider the problem:
Minimizef (x)=x^2 − 10 x− 1
subject to
1 ≤x≤ 10Plot the contours of theφkfunction using the linear extended interior penalty function
method.7.27 Consider the problem:
Minimizef (x 1 , x 2 )=(x 1 − 1 )^2 +(x 2 − 2 )^2subject to
2 x 1 −x 2 =0 and x 1 ≤ 5Construct theφkfunction according to the interior penalty function approach and complete
the minimization ofφ 1.