Cannot perform the operation: {concave} ./ {concave}

Nonconvex
1

Dear everyone:-)
I got some question when I tried to used cvx.
My code is followed:
clear;
clear all;
k = 8;
%n = [0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1];
n = 0.3;
r=0.9;%暂时假设
%仿真参数设置;
N0 = -147; Wul = 10000; Wdl = 10000;
Pumax = 100; Pdmax = 1000; Fc = 10^10;%dbm=10lg(P/1mw)
lu = 1.7810^-6; ld = 0.625;
BIk = 1000ones(1,k); BOk = 1000ones(1,k);
Vk = 2640BIk; Vs = nVk;
BOs = nBOk; BIs = nBIk;
%初始化z0 = [Pul,Bls,f,Pdl,PdM,TuS,TdS];
Pul0 = Pumaxrand(1,k); Bls0 = BIs/k; Pdl0 = Pdmaxrand(1,k); PdM0 = Pdmaxrand(1,1);
fk0 = rand(1,k); fs0 = rand(1,1); f0 = [fk0,fs0];

Rul0 = (Wul/k)log2(1+((rPul0)/10^((N0+10log10(Wul/k))-3)));
Rdl0 = (Wdl/k)log2(1+((rPdl0)/10^((N0+10log10(Wdl/k))-3)));
RdM0 = Wdllog2(1+((rPdM0)/10^((N0+10*log10(Wdl))-3)));

TuS0 = max(Bls0./Rul0); TdS0 = max(BOs./RdM0);

z0 = [Pul0,Bls0,f0,Pdl0,PdM0,TuS0,TdS0];
a = 10^-5; e = 10^-5;

%求解最优解
%cvx_solver mosek
cvx_begin
    %variable Pul(1,k) Bls(1,k) fk(1,k) fs Pdl(1,k) PdM TuS TdS;
    variable Pul(1,k);
    variable Bls(1,k);
    variable fk(1,k);
    variable Pdl(1,k);
    variable fs;
    variable PdM;
    variable TuS;
    variable TdS;
    f = [fk,fs];
    Rul = (Wul/k)*log(1+((r*Pul)/10^((N0+10*log(Wul/k))-3)))/log(2);
    Rdl = (Wdl/k)*log(1+((r*Pdl)/10^((N0+10*log(Wdl/k))-3)))/log(2);
    RdM = Wdl*log(1+((r*PdM)/10^((N0+10*log(Wdl))-3)))/log(2);
    
    %TuS = max(Bls.*inv_pos(Rul));
    %TdS = max(BOs.*inv_pos(RdM));
    %TuS = max(Bls./Rul);
    %TdS = max(BOs./RdM);        
    %Tmax = TuS+Vs/(fs*Fc)+TdS+max((BIk - Bls)/Rul+(Vk-Vs)/(fk*Fc)+(BOk-BOs)/Rdl);
    z = [Pul,Bls,f,Pdl,PdM,TuS,TdS];
    a = square_pos(Bls+inv_pos(Rul));
    b = square_pos(Rul0);
    c = Bls0.*(Bls-Bls0);
    d = 10^((N0+10*log10(Wul/k))-3);
    e = 1+(r*Pul0)*inv_pos(d).*square_pos(Rul0).*square_pos(Rul0);
    f = c-Rul0/e*(inv_pos(Rul)-inv_pos(Rul0));
    g = (a-square_pos(Bls0)-1./b);
    gk = 1/2*g-f;  
    %gk = 1/2*((Bls+1/Rul)^2-Bls0^2-1/Rul0^2)-(Bls0*(Bls-Bls0)-Rul0/((1+(r*Pul0)/10^((N0+10*log10(Wul/k))-3))*Rul0^4)*(1/Rul-1/Rul0));  
    Edl = ((BOk-BOs).*inv_pos(Rdl)+BOs*inv_pos(RdM))*ld;
    E = (z-z0)*diag(z0)*(z-z0)';
            
    a1 = Pul0.*(Bls0+(BIk-pos(Bls)))./Rul;
    b1 = Pul0.*(Bls+(BIk-Bls))./Rul0;
    c1 = Pul.*(Bls0+(BIk-Bls))./Rul0;
    d1 = lu*(Bls+(BIk-Bls));
    Eul = a1+b1+c+E+d1;
    minimize(sum(Eul+Edl))
    %minimize(sum(Pul0.*(Bls0+(BIk-Bls))./Rul+Pul0.*(Bls+(BIk-Bls))./Rul0+Pul.*(Bls0+(BIk-Bls))./Rul0+(z-z0)*diag(z-z0)+lu*(Bls+(BIk-Bls))+((BOk-BOs)./Rdl+BOs./RdM)*ld))
    subject to
        (BIk - Bls)/Rul+(Vk-Vs)/(fk*Fc)+Vs/(fs*Fc)+(BOk-BOs)/Rdl <= Tmax-TuS-TdS    %约束条件C.1
        gk <= TuS    %约束条件C.2
        BOs/RdM <= TdS    %约束条件C.3
        sum(fk) <= 1      %约束条件C.4
        fk >= 0
        0 <= fs <= 1
        sum(Bls) == BIs   %约束条件C.5
        sum(Pdl) <= Pdmax    %约束条件C.6
        PdM <= Pdmax
        Pul <= Pumax
cvx_end

The error is:
Error using cvx/times (line 173)

Disciplined convex programming error:
Cannot perform the operation: {concave} ./ {concave}

Error in cvx/rdivide (line 19)
z = times( x, y, ‘./’ );

Error in cvx_test (line 65)
a1 = Pul0.*(Bls0+(BIk-pos(Bls)))./Rul;

I would like to know if the objective function needs x and y to multiply or divide, how to convert it so that cvx can accept the model?

Can anyone give me some advice? Thank you!

Xiancan Lian

2

How have you proven that your problem is convex? If it is not convex, there is no possibility of entering it into CVX.

This question will be marked non-convex, unless you are able to show that it is convex.

3

Thanks Mark L. Stone. I have to make the simulation in a document, the formula in the document has been described as a convex function. My question now is how should I convert my target function into a form that cvx can recognize by using some function like rel_entr() and so on?
微信截图_20171018145605

4

Simply said. I have two variables x, y. They are vectors, the objective function is x/y. I transform them into a form x/y = entr(x)/(entr(y) - rel_entr(y,x)).
Does it work? Beacause I got the error like this:
Error using cvx/rel_entr (line 71)
Disciplined convex programming error:
Illegal operation: rel_entr( {concave}, {positive constant} ).

Error in entr (line 20)
y = -rel_entr( x, 1 );

Error in cvx_test (line 62)
A1 = entr(Bls)/(entr(Rul)-rel_entr(Rul,Bls));

5

You didn’t have entr or rel_entr in your first post. The image in your 2nd post is cut off. I don’t know what you are trying to do. What exactly is convex? You have so many different things in your posts that I don’t know what’s what.