multiobj_2009_10_21_02_2up

multiobj_2009_10_21_02_2up - 9-1 Multiobjective...

This preview shows pages 1–3. Sign up to view the full content.

9 - 1 Multiobjective Least-Squares S. Lall, Stanford 2009.10.21.02 9. Multiobjective Least-Squares Multi-objective least squares Trade-off curves Weighted-sum objectives Example: trade-off curve 9 - 2 Multiobjective Least-Squares S. Lall, Stanford 2009.10.21.02 Multi-Objective Least Squares in many problems we have two (or more) objectives we want J 1 = Ax y 2 small and also J 2 = Fx g 2 small usually the objectives are competing we can make one smaller at the expense of making the other larger common example: F = I, g = 0 : we want Ax y small, with small x

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
x (1) x (2) x (3) J 1 J 2 9 - 3 Multiobjective Least-Squares S. Lall, Stanford 2009.10.21.02 trade-off curve shaded area shows ( J 2 , J 1 ) achieved by some x R n clear area shows ( J 2 , J 1 ) not achieved by any x R n boundary of region is called optimal trade-off curve corresponding x called Pareto optimal (for the objectives Ax y 2 , Fx g 2 ) three example choices of x : x (1) , x (2) , x (3) x (3) is worse than x (2) on both counts ( J 2 and J 1
This is the end of the preview. Sign up to access the rest of the 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