70 lines
1.9 KiB
Mathematica
70 lines
1.9 KiB
Mathematica
|
function pcut = addBilinearVariableCuts(p)
|
||
|
|
|
||
|
|
if isempty(p.bilinears)
|
||
|
|
pcut = p;
|
||
|
|
else
|
||
|
|
pcut = emptyNumericalModel;
|
||
|
|
|
||
|
|
z = p.bilinears(:,1);
|
||
|
|
x = p.bilinears(:,2);
|
||
|
|
y = p.bilinears(:,3);
|
||
|
|
|
||
|
|
nn = length(p.c);
|
||
|
|
|
||
|
|
still_uncertain = find(abs(p.lb(z)-p.ub(z))>1e-8);
|
||
|
|
if ~isempty(still_uncertain)
|
||
|
|
|
||
|
|
x_lb = p.lb(x);
|
||
|
|
x_ub = p.ub(x);
|
||
|
|
y_lb = p.lb(y);
|
||
|
|
y_ub = p.ub(y);
|
||
|
|
m = length(x);
|
||
|
|
one = ones(m,1);
|
||
|
|
general_vals =[x_lb.*y_lb one -y_lb -x_lb,x_ub.*y_ub one -y_ub -x_ub,-x_ub.*y_lb -one y_lb x_ub,-x_lb.*y_ub -one y_ub x_lb]';
|
||
|
|
general_cols = [one z+1 x+1 y+1 one z+1 x+1 y+1 one z+1 x+1 y+1 one z+1 x+1 y+1]';
|
||
|
|
general_row = [1;1;1;1;2;2;2;2;3;3;3;3;4;4;4;4];
|
||
|
|
|
||
|
|
quadratic_row = [1;1;1;2;2 ;2;3; 3; 3;4;4;4;5;5;5;6;6;6];
|
||
|
|
quadratic_cols = [one z+1 x+1 ,one z+1 x+1 ,one z+1 x+1, one z+1 x+1 ,one z+1 x+1, one z+1 x+1]';
|
||
|
|
x1 = (3*x_ub+x_lb)/4;
|
||
|
|
x2 = (x_ub+3*x_lb)/4;
|
||
|
|
x3 = (x_ub+x_lb)/2;
|
||
|
|
quadratic_vals = [-x_ub.*x_lb -one x_lb+x_ub x_lb.*y_lb one -y_lb-x_lb x_ub.*y_ub one -y_ub-x_ub x1.*x1 one -x1-x1 x2.*x2 one -x2-x2 x3.*x3 one -x3-x3]';
|
||
|
|
m = 1+length(p.c);
|
||
|
|
rows = [];
|
||
|
|
cols = [];
|
||
|
|
vals = [];
|
||
|
|
nrow = 0;
|
||
|
|
|
||
|
|
for i =still_uncertain(:)'
|
||
|
|
x = p.bilinears(i,2);
|
||
|
|
y = p.bilinears(i,3);
|
||
|
|
if x~=y
|
||
|
|
rows = [rows;general_row+nrow];
|
||
|
|
vals = [vals;general_vals(:,i)];
|
||
|
|
cols = [cols;general_cols(:,i)];
|
||
|
|
nrow = nrow + 4;
|
||
|
|
else
|
||
|
|
col = quadratic_cols(:,i);
|
||
|
|
val = quadratic_vals(:,i);
|
||
|
|
|
||
|
|
rows = [rows;quadratic_row+nrow];
|
||
|
|
vals = [vals;val];
|
||
|
|
cols = [cols;col];
|
||
|
|
nrow = nrow + max(quadratic_row);
|
||
|
|
end
|
||
|
|
end
|
||
|
|
|
||
|
|
F_temp = sparse(rows,cols,vals,nrow,m);
|
||
|
|
keep = find(~isinf(F_temp(:,1)) & ~isnan(F_temp(:,1)));
|
||
|
|
F_temp = F_temp(keep,:);
|
||
|
|
pcut.F_struc = [F_temp;pcut.F_struc];
|
||
|
|
pcut.K.l = pcut.K.l+size(F_temp,1);
|
||
|
|
end
|
||
|
|
|
||
|
|
pcut = mergeNumericalModels(p,pcut);
|
||
|
|
end
|
||
|
|
|
||
|
|
|
||
|
|
|