# Objective: linear
# Constraints: convex nonlinear

function kth_diag;

param eps, default 0;

param n;
param m;

set N := {1..n};
set M := {1..m};

param A{i in N,j in N,M: j>=i}, default 0;
param C{i in N,j in N:   j>=i}, default 0;
param b{M}, default 0;

var X{i in N,j in N: j>=i};

minimize cost: sum {i in N, j in N: j>i} 2*C[i,j]*X[i,j] 
	                  + sum {j in N}   C[j,j]*X[j,j];

subject to equalities{k in M}:
    sum {i in N, j in N: j>i} 2*A[i,j,k]*X[i,j] 
               + sum {j in N}   A[j,j,k]*X[j,j]
    = b[k];

subject to pos_kth_diag{k in N}:
    kth_diag({i in N, j in N: j>=i} X[i,j]) >= eps;

data sdp.dat;

let {i in N, j in N: j>i} X[i,j] := 0;
let {i in N} X[i,i] := 1;

option presolve 0; # must be turned off for kth_diag to work properly
option loqo_options $loqo_options" convex sdp sigfig=6";
solve;

display X;
display equalities;