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Math Help - How to prove this value

  1. #1
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    Jan 2007
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    How to prove this value

    Max -logdet(S)
    st.(1)LMI>=0 , LMI=[S,Phi*S,Phi1*S,Phi2*S;(Phi*S)',S-r*S,0,0;(Phi1*S),0,r*S,0;

    (Phi2*S)',0,0,r*S];
    (2)S>0;
    (3)0<r<1;
    (4)K*S*K'<=um
    S is positive definite matrix variable;Phi,Phi1,Phi2,K,um is fixed.
    r is scalar variable.


    Because of the product of S and r, I can only maxmize the object by giving r

    ie. 20 value between 0 and 1 and run the program in matlab 20 times and find

    the largest objective in the 20 cycle. I find there is always a single r such that

    the objective is the largest. But I want to proof it in maths , I can not make it


    I try to use S prosedure but I can not.
    I also try to proof its convexity, but it seems useless.
    Do you have any better idea? Thanks very much
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  2. #2
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    Jan 2007
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    Sorry the objective should be Max logdet(S)
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