{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

assign04soln

# 4 54 given f x c x 1 x cx where 2 c 4 4 c 3

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: his becomes −2 u1 + 2u2 −4 = u1 , −5 u1 + 3u2 which has no solution. Therefore, x∗ is not optimal for this problem either. Thus, this QP code was only correct for one of the three test problems and therefore does not work properly. 4 (5.4) Given f (x) = c x + 1 x Cx, where 2 c= −4 −4 , C= 3 −1 −1 3 , the eigenvalues of C are λ = 2, with eigenvector s = (1, 1) , and λ = 4, with eigenvector s = (1, −1) . Therefore, we have S CS = D, where 1 S=√ 2 1 1 −1 1 , D= 2 0 0 4 . Solving Cx0 = −c, we have x0 = (2, 2) . Deﬁning y by x = Sy + x0 , we have 1 2 2 f (x) = f (x0 ) + y Dy = −8 + y1 + 2y2 . 2 Therefore, the level set for f (x) = −7 is given by 2 y1 + 2 y2 =1 1/2 1 which is an ellipse with intercepts at (±1, 0) and (0, ± √2 ) . The level set for f (x) = −4 is given by 2 2 y1 y2 + =1 4 2 √ which is an ellipse with intercepts at (±2, 0) and (0, ± 2) . 5 x2 ... y 5 ... 1 y.2 ..... .... ... ....... ......... 4 ......... .... ..... ...........................
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern