I need help to to make this work .I am using the quadprog function but i keep getting the problem is non convex.I would be glad if anyone could help.

function [x,IC,SST,SSR,SSE]=Constrained_FLSR_1(h)

D=[-0.04844752  0.041968141   -0.044564664   -0.050000004  -0.324629009  -0.148966655;
 -0.304020248  0.131284505    0.472041681    0.352249637   0.098999992   0.281067416;
 -0.074829705  -0.049999997  -0.094350919   -0.059151836   0.055000007  -0.154999971;
 0.28895241      0.390694469   0.416666657    0.408958316   0.497573376   0.360221535;
 -0.098011374  0.012270158  -0.067317739    -0.098011397   0.334000021  -0.120833755;
 -0.175849974  -0.160909101 -0.174713209    -0.200000003   0.022500008  -0.18519102;
 -0.141403094  -0.004999995 -0.098300003   -0.156213611  -0.048067875  -0.136289001;
 -0.210274339  -0.191784486 -0.109999985   -0.15615499  -0.070813216  -0.184634596];
% Large data set      
Large_Temp=[1:8];
Largetest=[1:8];
Large=union(Large_Temp,Largetest)

h=0.2;
OUT=D(Large,6)
IN=[ones(length(Large),1) D(Large,1:5)]
[M,N]=size(IN)

H=[2*sum(IN(:,1).^2),2*sum(IN(:,1).*IN(:,2)),2*sum(IN(:,3).*IN(:,1)),2*sum(IN(:,4).*IN(:,1)),2*sum(IN(:,5).*IN(:,1)),2*sum(IN(:,6).*IN(:,1)),0,0,0,0,0,0;
   2*sum(IN(:,1).*IN(:,2)),2*sum(IN(:,2).^2),2*sum(IN(:,3).*IN(:,2)),2*sum(IN(:,4).*IN(:,2)),2*sum(IN(:,5).*IN(:,2)),2*sum(IN(:,6).*IN(:,2)),0,0,0,0,0,0;
  2*sum(IN(:,1).*IN(:,3)),2*sum(IN(:,2).*IN(:,3)),2*sum(IN(:,3).^2), 2*sum(IN(:,4).*IN(:,3)) ,2*sum(IN(:,5).*IN(:,3)) ,2*sum(IN(:,6).*IN(:,3)),0,0,0,0,0,0;
   2*sum(IN(:,1).*IN(:,4)),2*sum(IN(:,2).*IN(:,4)),2*sum(IN(:,3).*IN(:,4)),2*sum(IN(:,4)).^2,2*sum(IN(:,5).*IN(:,4)),2*sum(IN(:,6).*IN(:,4)),0,0,0,0,0,0;
   2*sum(IN(:,1).*IN(:,5)),2*sum(IN(:,2).*IN(:,5)),2*sum(IN(:,3).*IN(:,5)),2*sum(IN(:,4).*IN(:,5)),2*sum(IN(:,5).^2),2*sum(IN(:,6).*IN(:,5)),0,0,0,0,0,0;
   2*sum(IN(:,1).*IN(:,6)),2*sum(IN(:,2).*IN(:,6)),2*sum(IN(:,3).*IN(:,6)),2*sum(IN(:,4).*IN(:,6)),2*sum(IN(:,5).*IN(:,6)),2*sum(IN(:,6).^2),0,0,0,0,0,0;
   0,0,0,0,0,0,(1/3)*sum(IN(:,1).^2),(1/3)*sum(IN(:,1).*IN(:,2)),(1/3)*sum(IN(:,1).*IN(:,3)),(1/3)*sum(IN(:,1).*IN(:,4)),(1/3)*sum(IN(:,1).*IN(:,5)),(1/3)*sum(IN(:,1).*IN(:,6));
   0,0,0,0,0,0,(1/3)*sum(IN(:,1).*IN(:,2)),(1/3)*sum(IN(:,2).^2),(1/3)*sum(IN(:,2).*IN(:,3)),(1/3)*sum(IN(:,2).*IN(:,4)),(1/3)*sum(IN(:,2).*IN(:,5)),(1/3)*sum(IN(:,2).*IN(:,6));
   0,0,0,0,0,0,(1/3)*sum(IN(:,1).*IN(:,3)),(1/3)*sum(IN(:,2).*IN(:,3)),(1/3)*sum(IN(:,3).^2),(1/3)*sum(IN(:,3).*IN(:,4)),(1/3)*sum(IN(:,3).*IN(:,5)),(1/3)*sum(IN(:,3).*IN(:,6));
   0,0,0,0,0,0,(1/3)*sum(IN(:,1).*IN(:,4)),(1/3)*sum(IN(:,2).*IN(:,4)),(1/3)*sum(IN(:,3).*IN(:,4)),(1/3)*sum(IN(:,4).^2),(1/3)*sum(IN(:,4).*IN(:,5)),(1/3)*sum(IN(:,4).*IN(:,6));
   0,0,0,0,0,0,(1/3)*sum(IN(:,1).*IN(:,5)),(1/3)*sum(IN(:,2).*IN(:,5)),(1/3)*sum(IN(:,3).*IN(:,5)),(1/3)*sum(IN(:,4).*IN(:,5)),(1/3)*sum(IN(:,5).^2),(1/3)*sum(IN(:,5).*IN(:,6));
   0,0,0,0,0,0,(1/3)*sum(IN(:,1).*IN(:,6)),(1/3)*sum(IN(:,2).*IN(:,6)),(1/3)*sum(IN(:,3).*IN(:,6)),(1/3)*sum(IN(:,4).*IN(:,6)),(1/3)*sum(IN(:,5).*IN(:,6)),(1/3)*sum(IN(:,5).^2);]
f=[-2*sum(OUT.*IN(:,1));-2*sum(OUT.*IN(:,2));-2*sum(OUT.*IN(:,3));-2*sum(OUT.*IN(:,4));-2*sum(OUT.*IN(:,5));-2*sum(OUT.*IN(:,5));0;0;0;0;0;0]

%A=[-IN -(1-h)*abs(IN);IN -(1-h)*abs(IN);zeros(N,2*N);zeros(N,N) -eye(N,N)]
A=[-IN -(1-h)*(IN);IN -(1-h)*(IN);zeros(N,N) -eye(N,N)]

   %b=[-OUT;OUT;zeros(2*N,1)];
  b=[-OUT;OUT;zeros(N,1)];

options = optimoptions('quadprog','Algorithm','interior-point-convex');
x=quadprog(H,f,A,b,[],[],[],[],[],options)

antec=x(1:6)
postc=x(7:12)
err=abs(((IN*(antec)-OUT)./OUT))

me=mean(err)
sum1=0;
for i=1:8
    sum1=sum1+(err(i,1)-me)^2;
end
voe=sum1/7

Answer 1

[Matt J]

Use fmincon instead. Quadprog cannot handle a non-convex objective with linear inequality constraints that are not simple bounds.

Also, for better performance, use the lb,ub arguments (not A,b) to express pure bounds.

[Honey Adams]

Thank you for your ur reply, but please can you explain your last statement further? A,b represents my linear inequalities. I have no bounds in this problem reason I used [],[] to represent them

[Matt J]

The final N constraints

A=[... ;zeros(N,N) -eye(N,N)]

    b=[.... ;zeros(N,1)];

are equivalent to saying that your final N variables must be non-negative. Those are pure bounds that you could use lb,ub to express.

[Honey Adams]

Thank you for your reply.I appreciate it. But the issue is I would like half of the N variables to be positive, the remaining could take on any variable. I am not defining the pure bounds for all the variables. That is why I defined the zeros for the first part of A=[... ;zeros(N,N) -eye(N,N)] .will this be ok lb=[-inf;-inf...;0;0..] ub=[]

[Matt J]

Yes, you can use all the constraint arguments (A,b,lb,ub,Aeq,beq) simultaneously and +/-Inf are legitimate values in lb,ub.

[Honey Adams]

Thank you.It worked.