Why do two optimization toolboxes produce two different results?

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Jack 2014-7-22

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https://ww2.mathworks.cn/matlabcentral/answers/142903-why-do-two-optimization-toolboxes-produce-two-different-results

关闭： Matt J 2014-7-22

W2 and G2.mat

I have a Quadratic Program to be solved:

min （h2-G2*phi2)'*W2*(h2-G2*phi2)

subject to: D*phi2>a

where h2=[109085.919608444 459933.363318136 100340.525393388 668230.037176691 175880.986764044 597041.601537766 186270.889983192 981230.967844572]';

W2 and G2 are too complex so that they are shown in figures:

The data is uploaded to the website.

I use “quadprog” and “SeDuMi” to solve the quadratic programming problems. But the results are different. The results are shown as follow:

SeDuMi: phi2 = [15.8407983652723 224712.855054258 49190.7060861108 -139558.381444911 -182685.449767951 -14593.7826296176]';

quadprog: phi2 = [0 224658.368498995 49166.3250817687 -139602.451899739 -182822.341031919 -14652.8624815402]';

In the two phi2 vectors shown above, the first elements are different, but other corresponding elements' values are similar.

Would you tell me the reason?

Thanks a lot, Jack

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Matt J 2014-7-22

编辑：Matt J 2014-7-22

This seems like an unnecessary duplicate of your post from last month

http://www.mathworks.com/matlabcentral/answers/134472-why-do-two-optimization-toolboxes-produce-two-different-results

You received answers there that that pretty much resolve the issue. You have multiple solutions (or approximately so), because the system is badly conditioned.

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