Root relaxation: unbounded when I use cvx with gurobi
ユーザーの入力を待っています。
I learned the problem "Root relaxation: unbounded" were caused the unbounded variables most likely. So I checked all variables but I didn't find the variables exsiting problem. I'm very confused because I need to solve the problem in finite time. I will be appreicated if you can help me.
The agent 4 is MIP optimization. Other agents is general QP optimization. When I run to the agent 4, the code stops running and keep busy. The control screen is as follows.
Calling Gurobi_2 9.12: 1108 variables, 650 equality constraints
------------------------------------------------------------
Gurobi Optimizer, licensed to CVX for CVX
Academic license - for non-commercial use only - expires 2023-03-10
Gurobi Optimizer version 9.1.2 build v9.1.2rc0 (win64)
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 650 rows, 1108 columns and 2740 nonzeros
Model fingerprint: 0x87c2d29d
Model has 98 quadratic constraints
Variable types: 1060 continuous, 48 integer (48 binary)
Coefficient statistics:
Matrix range [9e-04, 9e+01]
QMatrix range [1e+00, 1e+00]
Objective range [7e-25, 1e+02]
Bounds range [1e+00, 1e+00]
RHS range [3e-01, 9e+01]
Presolve removed 433 rows and 769 columns
Presolve time: 0.09s
Presolved: 703 rows, 1017 columns, 1852 nonzeros
Presolved model has 290 quadratic constraint(s)
Variable types: 897 continuous, 120 integer (24 binary)
Root relaxation: unbounded, 48 iterations, 0.00 seconds
I want to know what caused the problem eagerly. To faciliate you to understand the problem, I put complete codes as follows.
clear all; %#ok<CLALL>
close all;
clc;
n=4;m=24;
e_abs = 1e-4;e_rel = 1e-4; MAX_ITER = 500;%迭代次数
t =0.01;nu = 2; v=100;rho = 0.01;%change
MM=90;
X = zeros(n*m,n+1);
X_new = zeros(n*m,n+1);;lambda = zeros(n*m,2*(n+1));
h=ones(m,1);h1=zeros(m,1);
PV=[0, 0, 0, 0, 0, 0, 0, 37.46, 51.45, 56.01,58.06,85, 93, 82.98,51.59,29.70, 20.92, 0, 0, 0, 0, 0, 0, 0];
WT=[46.54,41.27,60.5,35,45, 54, 50, 45, 45.5, 40, 35, 0, 5, 4, 3, 6, 44.5, 48.04,40.5, 36.02,45.5,42.42, 44, 45.5];
d=[120.5,120, 150, 110, 130,131,130, 150.2, 280, 320.5,340,350.4,366.6,341.5, 240.2,220.6, 320.6,302.4,320.7, 208,180, 146.2, 119.6,105.3];
PW=PV+WT;Dd=d-PW;
%DG parameters
a1=0.02*h;a2=0.0175*h;a3=0.0625*h;a4=0.01*h;
a=[a1;a2;a3];A=diag(a);
A1=diag([a1;h1;h1;h1]); A2=diag([h1;a2;h1;h1]);A3=diag([h1;h1;a3;h1]);A4=diag([h1;h1;h1;a4]);
a5=2*h;a6=1.75*h;a7=1*h;
B1=[a5;h1;h1;h1];B2=[h1;a6;h1;h1];B3=[h1;h1;a7;h1];
B0=[a5;a6;a7];
% Bess parameters
SOC_0=0.5;SOC_min=0.15;SOC_max=0.85;n_d=0.95;n_c=0.95;
delta_t=1;E_r=1000;M=tril(ones(24));
%upper and lower bounds
lower1=50*h;lower2=20*h;lower3=15*h;lower4=0*h; Upper1=120*h;Upper2=80*h;Upper3=50*h;Upper4=60*h;
lower=[lower1;lower2;lower3;lower4;]; Upper=[Upper1;Upper2;Upper3;Upper4;];
%DG rate
r1L=-20*ones(m-1,1);r2L=-20*ones(m-1,1);r3L=-20*ones(m-1,1); r1U=20*ones(m-1,1);r2U=20*ones(m-1,1);r3U=20*ones(m-1,1);
R1L=[r1L;0];R2L=[r2L;0];R3L=[r3L;0]; R1U=[r1U;0];R2U=[r2U;0];R3U=[r3U;0];
m1=[-1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
m2=zeros(m,m);
M1=[m1,m2,m2,m2];M2=[m2,m1,m2,m2];M3=[m2,m2,m1,m2,];
H1=diag([h;h1;h1;h1]);H2=diag([h1;h;h1;h1]);H3=diag([h1;h1;h;h1]);H4=diag([h1;h1;h1;h]);
for k = 1:MAX_ITER
%Agent 1
% x-update
cvx_begin
variable x_1(n*m)
obj1=x_1'*A1*x_1+B1'*x_1;
for i=1:24
cs1=inv_pos(-lower1(1)+H1(i,:)*x_1)+ inv_pos(Upper1(1)-H1(i,:)*x_1);
obj1=obj1+cs1*(1/t);
end
obj2=0;
for j=1:23
rate1=M1*x_1;
cs2=inv_pos(-r1L(1)+rate1(j,:))+ inv_pos(r1U(1)-rate1(j,:));
obj2=obj2+cs2*(1/t);
end
minimize(obj1+obj2+ (lambda(:,1)-lambda(:,10))'*x_1+(lambda(:,2)-lambda(:,3))'*x_1+
rho* sum_square_abs(X(:,5)- x_1)+rho* sum_square_abs(X(:,2)- x_1))
cvx_end
disp(x_1);
%lambda-update
X_new(:,1) = x_1;
lambda(:,1) = lambda(:,1) -rho*(X(:,5)-X_new(:,1));
lambda(:,2) = lambda(:,2) -rho*(X(:,2)-X_new(:,1));
lambda_result1(n*m*(k-1)+1:n*m*k,1)=lambda(:,1);
lambda_result1(n*m*(k-1)+1:n*m*k,2)=lambda(:,2);
%Agent 2
% x-update
cvx_begin
variable x_2(n*m)
obj1=x_2'*A2*x_2+B2'*x_2;
for i=25:48
cs1=inv_pos(-lower2(1)+H2(i,:)*x_2)+ inv_pos(Upper2(1)-H2(i,:)*x_2);
obj1=obj1+cs1*(1/t);
end
obj2=0;
for j=1:23
rate2=M2*x_2;
cs2=inv_pos(-r2L(1)+rate2(j,:))+ inv_pos(r2U(1)-rate2(j,:));
obj2=obj2+cs2*(1/t);
end
minimize(obj1+obj2 +(lambda(:,3)-lambda(:,2))'*x_2+(lambda(:,4)-lambda(:,5))'*x_2+
rho* sum_square_abs(X(:,1)- x_2)+rho* sum_square_abs(X(:,3)- x_2))
cvx_end
disp(x_2);
%lambda-update
X_new(:,2) = x_2;
lambda(:,3) = lambda(:,3) -rho*(X(:,1)-X_new(:,2));
lambda(:,4) = lambda(:,4) -rho*(X(:,3)-X_new(:,2));
lambda_result1(n*m*(k-1)+1:n*m*k,3)=lambda(:,3);
lambda_result1(n*m*(k-1)+1:n*m*k,4)=lambda(:,4);
%Agent 3
% x-update
cvx_begin
variable x_3(n*m)
obj1=x_3'*A3*x_3+B3'*x_3;
for i=49:72
cs1=inv_pos(-lower3(1)+H3(i,:)*x_3)+ inv_pos(Upper3(1)-H3(i,:)*x_3);
obj1=obj1+cs1*(1/t);
end
obj2=0;
for j=1:23
rate3=M3*x_3;
cs2=inv_pos(-r3L(1)+rate3(j,:))+ inv_pos(r3U(1)-rate3(j,:));
obj2=obj2+cs2*(1/t);
end
minimize(obj1+obj2 +(lambda(:,5)-lambda(:,4))'*x_3+(lambda(:,6)-lambda(:,7))'*x_3+
rho* sum_square_abs(X(:,2)- x_3)+rho* sum_square_abs(X(:,4)- x_3))
cvx_end
disp(x_3);
%lambda-update
X_new(:,3) = x_3;
lambda(:,5) = lambda(:,5) -rho*(X(:,2)-X_new(:,3));
lambda(:,6) = lambda(:,6) -rho*(X(:,4)-X_new(:,3));
lambda_result1(n*m*(k-1)+1:n*m*k,5)=lambda(:,5);
lambda_result1(n*m*(k-1)+1:n*m*k,6)=lambda(:,6);
%Agent 4
% x-update
cvx_begin
cvx_solver Gurobi_2
variable xx(1,m) binary
variable yy(1,m) binary
variables x_41(n*m) x_42(n*m) x_4(n*m)
variables z1(1,m) z2(1,m)
obj1=0;
for i=73:96
cs1=inv_pos(-lower4(1)+H4(i,:)*x_4)+ inv_pos(Upper4(1)-H4(i,:)*x_4);
obj1=obj1+cs1*(1/t);
end
obj2=0;
for j=1:24
rate5=-(delta_t/E_r)*M*(1/n_d*z1'-n_c*z2');
cs2=inv_pos(-SOC_min+SOC_0+rate5(j,:))+ inv_pos(SOC_max-SOC_0-rate5(j,:));
obj2=obj2+cs2*(1/t);
end
obj3=z1*ones(m,1)+z2*ones(m,1);
minimize(obj1+obj2+obj3+(lambda(:,7)-lambda(:,6))'*x_4
+(lambda(:,8)-lambda(:,9))'*x_4+rho* sum_square_abs(X(:,3)- x_4)+rho* sum_square_abs(X(:,5)- x_4))
subject to
for i=1:24
z1(i)<=xx(i)*Upper4(1);
z1(i)<=x_41(72+i);
z1(i)>=x_41(72+i)-(1-xx(i))*Upper4(1)
0<=z1(i)<=Upper4(1);
lower4(1)<=x_41(72+i)<=Upper4(1);
z2(i)<=yy(i)*Upper4(1);
z2(i)<=x_42(72+i);
z2(i)>=x_42(72+i)-(1-yy(i))*Upper4(1)
0<=z2(i)<=Upper4(1);
lower4(1)<=x_42(72+i)<=Upper4(1);
-MM*(1-xx(i))<=x_4(72+i)-x_41(72+i)<=MM*(1-xx(i));
-MM*(1-yy(i))<=x_4(72+i)+x_42(72+i)<=MM*(1-yy(i));
xx(i)+yy(i)==1;
end
cvx_end
disp(x_4);
%lambda-update
X_new(:,4) = x_4;
lambda(:,7) = lambda(:,7) -rho*(X(:,3)-X_new(:,4));
lambda(:,8) = lambda(:,8) -rho*(X(:,5)-X_new(:,4));
lambda_result1(n*m*(k-1)+1:n*m*k,7)=lambda(:,7);
lambda_result1(n*m*(k-1)+1:n*m*k,8)=lambda(:,8);
%Agent 5
% x-update
cvx_begin
variable x_5(n*m)
F1=x_5(1,:)+x_5(24+1,:)+x_5(2*24+1,:)+x_5(3*24+1,:);F6=x_5(6,:)+x_5(24+6,:)+x_5(2*24+6,:)+x_5(3*24+6,:);
F2=x_5(2,:)+x_5(24+2,:)+x_5(2*24+2,:)+x_5(3*24+2,:);F7=x_5(7,:)+x_5(24+7,:)+x_5(2*24+7,:)+x_5(3*24+7,:);
F3=x_5(3,:)+x_5(24+3,:)+x_5(2*24+3,:)+x_5(3*24+3,:);F8=x_5(8,:)+x_5(24+8,:)+x_5(2*24+8,:)+x_5(3*24+8,:);
F4=x_5(4,:)+x_5(24+4,:)+x_5(2*24+4,:)+x_5(3*24+4,:);F9=x_5(9,:)+x_5(24+9,:)+x_5(2*24+9,:)+x_5(3*24+9,:);
F5=x_5(5,:)+x_5(24+5,:)+x_5(2*24+5,:)+x_5(3*24+5,:);F10=x_5(10,:)+x_5(24+10,:)+x_5(2*24+10,:)+x_5(3*24+10,:);
F11=x_5(11,:)+x_5(24+11,:)+x_5(2*24+11,:)+x_5(3*24+11,:);F16=x_5(16,:)+x_5(24+16,:)+x_5(2*24+16,:)+x_5(3*24+16,:);
F12=x_5(12,:)+x_5(24+12,:)+x_5(2*24+12,:)+x_5(3*24+12,:);F17=x_5(17,:)+x_5(24+17,:)+x_5(2*24+17,:)+x_5(3*24+17,:);
F13=x_5(13,:)+x_5(24+13,:)+x_5(2*24+13,:)+x_5(3*24+13,:);F18=x_5(18,:)+x_5(24+18,:)+x_5(2*24+18,:)+x_5(3*24+18,:);
F14=x_5(14,:)+x_5(24+14,:)+x_5(2*24+14,:)+x_5(3*24+14,:);F19=x_5(19,:)+x_5(24+19,:)+x_5(2*24+19,:)+x_5(3*24+19,:);
F15=x_5(15,:)+x_5(24+15,:)+x_5(2*24+15,:)+x_5(3*24+15,:);F20=x_5(20,:)+x_5(24+20,:)+x_5(2*24+20,:)+x_5(3*24+20,:);
F21=x_5(21,:)+x_5(24+21,:)+x_5(2*24+21,:)+x_5(3*24+21,:);F23=x_5(23,:)+x_5(24+23,:)+x_5(2*24+23,:)+x_5(3*24+23,:);
F22=x_5(22,:)+x_5(24+22,:)+x_5(2*24+22,:)+x_5(3*24+22,:);F24=x_5(24,:)+x_5(24+24,:)+x_5(2*24+24,:)+x_5(3*24+24,:);
FF=[F1,F2,F3,F4,F5,F6,F7,F8,F9,F10,F11,F12,F13,F14,F15,F16,F17,F18,F19,F20,F21,F22,F23,F24];
minimize(v*sum_square_abs(FF-Dd)+(lambda(:,9)-lambda(:,8))'*x_5
+(lambda(:,10)-lambda(:,1))'*x_5+rho* sum_square_abs(X(:,4)- x_5)+rho* sum_square_abs(X(:,1)- x_5))
cvx_end
disp(x_5);
%lambda-update
X_new(:,5) = x_5;
lambda(:,9) = lambda(:,9) -rho*(X(:,4)-X_new(:,5));
lambda(:,10) = lambda(:,10) -rho*(X(:,1)-X_new(:,5));
lambda_result1(n*m*(k-1)+1:n*m*k,9)=lambda(:,9);
lambda_result1(n*m*(k-1)+1:n*m*k,10)=lambda(:,10);
X = X_new;
for i = 1:n+1
X_result1(n*m*(k-1)+1:n*m*k,i) = X(:,i);
end
result(k)=x_1'*A1*x_1+B1'*x_1+x_2'*A2*x_2+B2'*x_2+x_3'*A3*x_3+B3'*x_3+x_4'*A4*x_4;
disp(result(k));
% Stop Criteria
if( k > 1)
for j = 1 : 5
if( j == 1 )
e_p(j) = norm( X(:,5) - X(:,1) ) + norm( X(:,2) - X(:,1) );
e_pri(j) = e_abs + ( max( norm( X(:,5) ) , max(norm( X(:,1) ) , norm(X(:,2)) ) ) ) * e_rel ;
end
if( j == 5)
e_p(j) = norm( X(:,4) - X(:,5) ) + norm( X(:,1) - X(:,5) );
e_pri(j) = e_abs + ( max( norm( X(:,4) ) , max( norm( X(:,5) ) , norm(X(:,1)) ) ) ) * e_rel ;
end
if(j~=1 && j~=5)
e_p(j) = norm( X(:,j-1) - X(:,j) ) + norm( X(:,j+1) - X(:,j) );
e_pri(j) = e_abs + ( max( norm( X(:,j-1) ) , max( norm( X(:,j) ) , norm(X(:,j+1)) ) ) ) * e_rel ;
end
e_d(j) = rho * norm( X_result1(n*m*(k-2)+1:n*m*(k-1),j) - X(:,j) );
e_dual(j) = e_abs + ( max( norm(lambda(:,2*j-1)) , norm(lambda(:,2*j)) ) ) * e_rel ;
end
if( (sum(e_p <= e_pri) ==5) && ( sum(e_d <= e_dual) == 5 ) )
break
end
end
t = nu*t;
end
-
-
Gurobi Staff
Posting the whole code does not help in analyzing the issue. It is always best to provide a minimal working example and use one of Gurobi's native APIs instead of 3rd party software such as CVXPY.
I cannot see where you set finite bounds for all your variables. Could you try setting finite lower and upper bounds for all variables? Setting upper bounds of, e.g., 1e4 should be enough. Gurobi sets a default lower bound of 0 so you don't have to set those.
Best regards,
Jaromił0 -
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