My SPD problem can be solved by SDPT3 solver but not SeDuMi solver?

kevin1 · July 17, 2014, 7:48pm

when i use the SDPT3, my problem can be correctly solved. but when i use SeDuMI as the solver, it can’t solve the problem (final result is ‘NaN’)and give an error message:

Status: Error
Optimal value (cvx_optval): NaN
 
Reference to non-existent field 'r0'.
Error in cvx_sedumi>solve (line 258)
tol = info.r0;
Error in cvxprob/solve (line 422)
            [ x, status, tprec, iters, y ] = shim.solve( At, b, c, cones,
            quiet, prec, solv.settings, eargs{:} );
Error in cvx_end (line 87)
        solve( prob );
Error in nlos_miti_toa_sdp_m_receivers (line 174)
                cvx_end;

The source code:

% clear;close all;

tic timestart=tic

%Parameters definition %observation times (OR observation times in one estimation) N=1; %repeat times for MSE calculation L=1; % noise VARIANCE = sqrt( var(x) ) VARIANCE=.01; %Fixed target position x_target=[-0.6 -0.3 0 0.3 0.6]; y_target=[-0.6 -0.3 0 0.3 0.6]; %anchor position anchor_posi=[1 1.414 1 0 -1 -1.414 -1 0 %x1 x2 x3 x4 1 0 -1 -1.414 -1 0 1 1.414]; %y1 y2 y3 y4 % anchor_posi=[1 2 1 2 -1 -2 -1 -2 %x1 x2 x3 x4 % 1 2 -1 -2 -1 2 1 2]; %y1 y2 y3 y4 % number of anchors M=length(anchor_posi(1,:)); %maximal nlos error. NLOS_MAX_RANGE = VARIANCE*20;

figure plot(-1,1, 'k');hold on;plot( -1,-1,'k');plot( 1,1,'k');plot(1,-1,'k') plot(1.414,0, 'k');plot( 0,-1.414,'k');plot(-1.414,0,'k');plot(0,1.414,'k') legend 'target position' grid on; for i=1:5 for j=1:5 plot(x_target(i), x_target(j),'r');hold on; index=(i-1)5+j; s=num2str(index); text(x_target(i)+0.05, x_target(j),s) end end

v=zeros(8,1); u=zeros(8,1); d1_observe = zeros(1,N); d2_observe = zeros(1,N); d3_observe = zeros(1,N); d4_observe = zeros(1,N); d5_observe = zeros(1,N); d6_observe = zeros(1,N); d7_observe = zeros(1,N); d8_observe = zeros(1,N);

mse_final_L=[]; %repeat for L times to calculate the MSE for l=1:L mse_final = [ ];

% input generation
%all kinds of conbination of NLOS for 8 receivers
mm=random('unif',0,1,[20,8]);% 'unif' UNIFORM distribution; 'exp' or 'Exponential'; 'norm' or 'Normal';
gain_tmp=[0 0 0 0 0 0 0 0 %1 0 1-25
    1 0 0 0 0 0 0 0 %2 1 26-50
    1 1 0 0 0 0 0 0 %3 2 51-175
    1 0 1 0 0 0 0 0 %4
    1 0 0 1 0 0 0 0 %5
    1 0 0 0 1 0 0 0 %6
    1 0 0 0 0 1 0 0 %7
    1 1 1 0 0 0 0 0 %8 3 176-275
    1 1 0 1 0 0 0 0 %9
    1 1 0 0 1 0 0 0 %10
    1 1 0 0 0 1 0 0 %11
    1 1 1 1 0 0 0 0 %12 4 276-350
    1 1 1 0 1 0 0 0 %13
    1 1 1 0 0 1 0 0 %14
    1 1 1 1 1 0 0 0 %15 5 351-400
    1 1 1 1 0 1 0 0 %16
    1 1 1 1 1 1 0 0 %17 6 401-450
    1 1 1 1 1 0 1 0 %18
    1 1 1 1 1 1 1 0 %19 7 451-475
    1 1 1 1 1 1 1 1 %20 8 476-500
    ];
gain = gain_tmp.*mm;
[m,n]=size(gain);



comb_c=[];
index_c=[];
comb_c_final=[];
index_c_final=[];


%for different combinations of NLOS
for comb=1:m


    % repeat for 5x5=25 different target positions estimation
    for t_x=1:5
        for t_y=1:5
            % N times of observations, should be iid, white nosie
            d1_observe = ((anchor_posi(1,1)-x_target(t_x))^2 + (anchor_posi(2,1)-y_target(t_y))^2)^0.5 + VARIANCE.*randn(N,1)+NLOS_MAX_RANGE*gain(comb,1);
            d2_observe = ((anchor_posi(1,2)-x_target(t_x))^2 + (anchor_posi(2,2)-y_target(t_y))^2)^0.5 + VARIANCE.*randn(N,1)+NLOS_MAX_RANGE*gain(comb,2);
            d3_observe = ((anchor_posi(1,3)-x_target(t_x))^2 + (anchor_posi(2,3)-y_target(t_y))^2)^0.5 + VARIANCE.*randn(N,1)+NLOS_MAX_RANGE*gain(comb,3);
            d4_observe = ((anchor_posi(1,4)-x_target(t_x))^2 + (anchor_posi(2,4)-y_target(t_y))^2)^0.5 + VARIANCE.*randn(N,1)+NLOS_MAX_RANGE*gain(comb,4);
            d5_observe = ((anchor_posi(1,5)-x_target(t_x))^2 + (anchor_posi(2,5)-y_target(t_y))^2)^0.5 + VARIANCE.*randn(N,1)+NLOS_MAX_RANGE*gain(comb,5);
            d6_observe = ((anchor_posi(1,6)-x_target(t_x))^2 + (anchor_posi(2,6)-y_target(t_y))^2)^0.5 + VARIANCE.*randn(N,1)+NLOS_MAX_RANGE*gain(comb,6);
            d7_observe = ((anchor_posi(1,7)-x_target(t_x))^2 + (anchor_posi(2,7)-y_target(t_y))^2)^0.5 + VARIANCE.*randn(N,1)+NLOS_MAX_RANGE*gain(comb,7);
            d8_observe = ((anchor_posi(1,8)-x_target(t_x))^2 + (anchor_posi(2,8)-y_target(t_y))^2)^0.5 + VARIANCE.*randn(N,1)+NLOS_MAX_RANGE*gain(comb,8);



            %%%%%%%%%%%%%%%%%%%%%%%%%% cvx %%%%%%%%%%%%%%%%%%%%%%%%%%%                
            v=[1 1 1 1 1 1 1 1];
            alf=.1;
            u=[0.2 0.2  0.2  0.2 0.2 0.2  0.2  0.2];

            cvx_begin sdp %quiet
            cvx_solver sedumi
            variable x(2,1)
            variable c(8,1)
            variable z
            variable h(8,1)

            minimize  v(1)*(d1_observe^2-h(1)-c(1))^2+alf*c(1)^2...
                +v(2)*(d2_observe^2-h(2)-c(2))^2+alf*c(2)^2...
                +v(3)*(d3_observe^2-h(3)-c(3))^2+alf*c(3)^2...
                +v(4)*(d4_observe^2-h(4)-c(4))^2+alf*c(4)^2...
                +v(5)*(d5_observe^2-h(5)-c(5))^2+alf*c(5)^2...
                +v(6)*(d6_observe^2-h(6)-c(6))^2+alf*c(6)^2...
                +v(7)*(d7_observe^2-h(7)-c(7))^2+alf*c(7)^2...
                +v(8)*(d8_observe^2-h(8)-c(8))^2+alf*c(8)^2;

            subject to

            h(1)==[anchor_posi(1,1)  anchor_posi(2,1)  -1]*[ 1 0 x(1);0 1 x(2);x(1) x(2) z]*[anchor_posi(1,1); anchor_posi(2,1);-1];
            h(2)==[anchor_posi(1,2)  anchor_posi(2,2)  -1]*[ 1 0 x(1);0 1 x(2);x(1) x(2) z]*[anchor_posi(1,2); anchor_posi(2,2);-1];
            h(3)==[anchor_posi(1,3)  anchor_posi(2,3)  -1]*[ 1 0 x(1);0 1 x(2);x(1) x(2) z]*[anchor_posi(1,3); anchor_posi(2,3);-1];
            h(4)==[anchor_posi(1,4)  anchor_posi(2,4)  -1]*[ 1 0 x(1);0 1 x(2);x(1) x(2) z]*[anchor_posi(1,4); anchor_posi(2,4);-1];
            h(5)==[anchor_posi(1,5)  anchor_posi(2,5)  -1]*[ 1 0 x(1);0 1 x(2);x(1) x(2) z]*[anchor_posi(1,5); anchor_posi(2,5);-1];
            h(6)==[anchor_posi(1,6)  anchor_posi(2,6)  -1]*[ 1 0 x(1);0 1 x(2);x(1) x(2) z]*[anchor_posi(1,6); anchor_posi(2,6);-1];
            h(7)==[anchor_posi(1,7)  anchor_posi(2,7)  -1]*[ 1 0 x(1);0 1 x(2);x(1) x(2) z]*[anchor_posi(1,7); anchor_posi(2,7);-1];
            h(8)==[anchor_posi(1,8)  anchor_posi(2,8)  -1]*[ 1 0 x(1);0 1 x(2);x(1) x(2) z]*[anchor_posi(1,8); anchor_posi(2,8);-1];

            [1 0 anchor_posi(1,1)-x(1);0 1 anchor_posi(2,1)-x(2);anchor_posi(1,1)-x(1) anchor_posi(2,1)-x(2) d1_observe^2+u(1)]>=0;
            [1 0 anchor_posi(1,2)-x(1);0 1 anchor_posi(2,2)-x(2);anchor_posi(1,2)-x(1) anchor_posi(2,2)-x(2) d2_observe^2+u(2)]>=0;
            [1 0 anchor_posi(1,3)-x(1);0 1 anchor_posi(2,3)-x(2);anchor_posi(1,3)-x(1) anchor_posi(2,3)-x(2) d3_observe^2+u(3)]>=0;
            [1 0 anchor_posi(1,4)-x(1);0 1 anchor_posi(2,4)-x(2);anchor_posi(1,4)-x(1) anchor_posi(2,4)-x(2) d4_observe^2+u(4)]>=0;
            [1 0 anchor_posi(1,5)-x(1);0 1 anchor_posi(2,5)-x(2);anchor_posi(1,5)-x(1) anchor_posi(2,5)-x(2) d5_observe^2+u(5)]>=0;
            [1 0 anchor_posi(1,6)-x(1);0 1 anchor_posi(2,6)-x(2);anchor_posi(1,6)-x(1) anchor_posi(2,6)-x(2) d6_observe^2+u(6)]>=0;
            [1 0 anchor_posi(1,7)-x(1);0 1 anchor_posi(2,7)-x(2);anchor_posi(1,7)-x(1) anchor_posi(2,7)-x(2) d7_observe^2+u(7)]>=0;
            [1 0 anchor_posi(1,8)-x(1);0 1 anchor_posi(2,8)-x(2);anchor_posi(1,8)-x(1) anchor_posi(2,8)-x(2) d8_observe^2+u(8)]>=0;

            [1 0 x(1);0 1 x(2);x(1) x(2) z]>=0;

            c(1)>=0;
            c(2)>=0;
            c(3)>=0;
            c(4)>=0;
            c(5)>=0;
            c(6)>=0;
            c(7)>=0;
            c(8)>=0;
            cvx_end;
%%%%%%%%%%%%%%%%%%%%%%%%%% end cvx %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

            x_estimated=x(1);y_estimated=x(2);              
            %final MSE calculation mse(real position, estimated position)
            mse_tmp = ((x_estimated - x_target(t_x))^2 + (y_estimated - y_target(t_y))^2)^0.5;
            mse_final = [mse_final mse_tmp];


        end
    end
end
mse_final_L=[mse_final_L;mse_final];
end timestop = toc

mse_final_L_f=sum(mse_final_L)/L;

figure plot(mse_final_L_f,'-.bo'); legend ('mse final'); xlabel 'target index'; ylabel 'MSE'; title 'MSE'

kevin1 · July 17, 2014, 8:03pm

THE SOURCE CODES:

%
clear;close all;

tic
timestart=tic

%Parameters definition
%observation times (OR observation times in one estimation)
N=1;
%repeat times for MSE calculation
L=1;
% noise VARIANCE = sqrt( var(x) )
VARIANCE=.01;
%Fixed target position
x_target=[-0.6 -0.3 0 0.3 0.6];
y_target=[-0.6 -0.3 0 0.3 0.6];
%anchor position
anchor_posi=[1 1.414 1 0 -1 -1.414 -1 0 %x1 x2 x3 x4
1 0 -1 -1.414 -1 0 1 1.414]; %y1 y2 y3 y4
% anchor_posi=[1 2 1 2 -1 -2 -1 -2 %x1 x2 x3 x4
% 1 2 -1 -2 -1 2 1 2]; %y1 y2 y3 y4
% number of anchors
M=length(anchor_posi(1,:));
%maximal nlos error.
NLOS_MAX_RANGE = VARIANCE*20;

figure
plot(-1,1, ‘k*’);hold on;plot( -1,-1,‘k*’);plot( 1,1,‘k*’);plot(1,-1,‘k*’)
plot(1.414,0, ‘k*’);plot( 0,-1.414,‘k*’);plot(-1.414,0,‘k*’);plot(0,1.414,‘k*’)
legend 'target position’
grid on;
for i=1:5
for j=1:5
plot(x_target(i), x_target(j),‘r*’);hold on;
index=(i-1)*5+j;
s=num2str(index);
text(x_target(i)+0.05, x_target(j),s)
end
end

v=zeros(8,1);
u=zeros(8,1);
d1_observe = zeros(1,N);
d2_observe = zeros(1,N);
d3_observe = zeros(1,N);
d4_observe = zeros(1,N);
d5_observe = zeros(1,N);
d6_observe = zeros(1,N);
d7_observe = zeros(1,N);
d8_observe = zeros(1,N);

mse_final_L=[];
%repeat for L times to calculate the MSE
for l=1:L
mse_final = [ ];

% input generation
%all kinds of conbination of NLOS for 8 receivers
mm=random('unif',0,1,[20,8]);% 'unif' UNIFORM distribution; 'exp' or 'Exponential'; 'norm' or 'Normal';
gain_tmp=[0 0 0 0 0 0 0 0 %1 0 1-25
    1 0 0 0 0 0 0 0 %2 1 26-50
    1 1 0 0 0 0 0 0 %3 2 51-175
    1 0 1 0 0 0 0 0 %4
    1 0 0 1 0 0 0 0 %5
    1 0 0 0 1 0 0 0 %6
    1 0 0 0 0 1 0 0 %7
    1 1 1 0 0 0 0 0 %8 3 176-275
    1 1 0 1 0 0 0 0 %9
    1 1 0 0 1 0 0 0 %10
    1 1 0 0 0 1 0 0 %11
    1 1 1 1 0 0 0 0 %12 4 276-350
    1 1 1 0 1 0 0 0 %13
    1 1 1 0 0 1 0 0 %14
    1 1 1 1 1 0 0 0 %15 5 351-400
    1 1 1 1 0 1 0 0 %16
    1 1 1 1 1 1 0 0 %17 6 401-450
    1 1 1 1 1 0 1 0 %18
    1 1 1 1 1 1 1 0 %19 7 451-475
    1 1 1 1 1 1 1 1 %20 8 476-500
    ];
gain = gain_tmp.*mm;
[m,n]=size(gain);



comb_c=[];
index_c=[];
comb_c_final=[];
index_c_final=[];


%for different combinations of NLOS
for comb=1:m
    

    % repeat for 5x5=25 different target positions estimation
    for t_x=1:5
        for t_y=1:5
            % N times of observations, should be iid, white nosie
            d1_observe = ((anchor_posi(1,1)-x_target(t_x))^2 + (anchor_posi(2,1)-y_target(t_y))^2)^0.5 + VARIANCE.*randn(N,1)+NLOS_MAX_RANGE*gain(comb,1);
            d2_observe = ((anchor_posi(1,2)-x_target(t_x))^2 + (anchor_posi(2,2)-y_target(t_y))^2)^0.5 + VARIANCE.*randn(N,1)+NLOS_MAX_RANGE*gain(comb,2);
            d3_observe = ((anchor_posi(1,3)-x_target(t_x))^2 + (anchor_posi(2,3)-y_target(t_y))^2)^0.5 + VARIANCE.*randn(N,1)+NLOS_MAX_RANGE*gain(comb,3);
            d4_observe = ((anchor_posi(1,4)-x_target(t_x))^2 + (anchor_posi(2,4)-y_target(t_y))^2)^0.5 + VARIANCE.*randn(N,1)+NLOS_MAX_RANGE*gain(comb,4);
            d5_observe = ((anchor_posi(1,5)-x_target(t_x))^2 + (anchor_posi(2,5)-y_target(t_y))^2)^0.5 + VARIANCE.*randn(N,1)+NLOS_MAX_RANGE*gain(comb,5);
            d6_observe = ((anchor_posi(1,6)-x_target(t_x))^2 + (anchor_posi(2,6)-y_target(t_y))^2)^0.5 + VARIANCE.*randn(N,1)+NLOS_MAX_RANGE*gain(comb,6);
            d7_observe = ((anchor_posi(1,7)-x_target(t_x))^2 + (anchor_posi(2,7)-y_target(t_y))^2)^0.5 + VARIANCE.*randn(N,1)+NLOS_MAX_RANGE*gain(comb,7);
            d8_observe = ((anchor_posi(1,8)-x_target(t_x))^2 + (anchor_posi(2,8)-y_target(t_y))^2)^0.5 + VARIANCE.*randn(N,1)+NLOS_MAX_RANGE*gain(comb,8);
            
            
            
            %%%%%%%%%%%%%%%%%%%%%%%%%% cvx %%%%%%%%%%%%%%%%%%%%%%%%%%%                
            v=[1 1 1 1 1 1 1 1];
            alf=.1;
            u=[0.2 0.2  0.2  0.2 0.2 0.2  0.2  0.2];

            cvx_begin sdp %quiet
            cvx_solver sedumi
            variable x(2,1)
            variable c(8,1)
            variable z
            variable h(8,1)
            
            minimize  v(1)*(d1_observe^2-h(1)-c(1))^2+alf*c(1)^2...
                +v(2)*(d2_observe^2-h(2)-c(2))^2+alf*c(2)^2...
                +v(3)*(d3_observe^2-h(3)-c(3))^2+alf*c(3)^2...
                +v(4)*(d4_observe^2-h(4)-c(4))^2+alf*c(4)^2...
                +v(5)*(d5_observe^2-h(5)-c(5))^2+alf*c(5)^2...
                +v(6)*(d6_observe^2-h(6)-c(6))^2+alf*c(6)^2...
                +v(7)*(d7_observe^2-h(7)-c(7))^2+alf*c(7)^2...
                +v(8)*(d8_observe^2-h(8)-c(8))^2+alf*c(8)^2;
            
            subject to
            
            h(1)==[anchor_posi(1,1)  anchor_posi(2,1)  -1]*[ 1 0 x(1);0 1 x(2);x(1) x(2) z]*[anchor_posi(1,1); anchor_posi(2,1);-1];
            h(2)==[anchor_posi(1,2)  anchor_posi(2,2)  -1]*[ 1 0 x(1);0 1 x(2);x(1) x(2) z]*[anchor_posi(1,2); anchor_posi(2,2);-1];
            h(3)==[anchor_posi(1,3)  anchor_posi(2,3)  -1]*[ 1 0 x(1);0 1 x(2);x(1) x(2) z]*[anchor_posi(1,3); anchor_posi(2,3);-1];
            h(4)==[anchor_posi(1,4)  anchor_posi(2,4)  -1]*[ 1 0 x(1);0 1 x(2);x(1) x(2) z]*[anchor_posi(1,4); anchor_posi(2,4);-1];
            h(5)==[anchor_posi(1,5)  anchor_posi(2,5)  -1]*[ 1 0 x(1);0 1 x(2);x(1) x(2) z]*[anchor_posi(1,5); anchor_posi(2,5);-1];
            h(6)==[anchor_posi(1,6)  anchor_posi(2,6)  -1]*[ 1 0 x(1);0 1 x(2);x(1) x(2) z]*[anchor_posi(1,6); anchor_posi(2,6);-1];
            h(7)==[anchor_posi(1,7)  anchor_posi(2,7)  -1]*[ 1 0 x(1);0 1 x(2);x(1) x(2) z]*[anchor_posi(1,7); anchor_posi(2,7);-1];
            h(8)==[anchor_posi(1,8)  anchor_posi(2,8)  -1]*[ 1 0 x(1);0 1 x(2);x(1) x(2) z]*[anchor_posi(1,8); anchor_posi(2,8);-1];
            
            [1 0 anchor_posi(1,1)-x(1);0 1 anchor_posi(2,1)-x(2);anchor_posi(1,1)-x(1) anchor_posi(2,1)-x(2) d1_observe^2+u(1)]>=0;
            [1 0 anchor_posi(1,2)-x(1);0 1 anchor_posi(2,2)-x(2);anchor_posi(1,2)-x(1) anchor_posi(2,2)-x(2) d2_observe^2+u(2)]>=0;
            [1 0 anchor_posi(1,3)-x(1);0 1 anchor_posi(2,3)-x(2);anchor_posi(1,3)-x(1) anchor_posi(2,3)-x(2) d3_observe^2+u(3)]>=0;
            [1 0 anchor_posi(1,4)-x(1);0 1 anchor_posi(2,4)-x(2);anchor_posi(1,4)-x(1) anchor_posi(2,4)-x(2) d4_observe^2+u(4)]>=0;
            [1 0 anchor_posi(1,5)-x(1);0 1 anchor_posi(2,5)-x(2);anchor_posi(1,5)-x(1) anchor_posi(2,5)-x(2) d5_observe^2+u(5)]>=0;
            [1 0 anchor_posi(1,6)-x(1);0 1 anchor_posi(2,6)-x(2);anchor_posi(1,6)-x(1) anchor_posi(2,6)-x(2) d6_observe^2+u(6)]>=0;
            [1 0 anchor_posi(1,7)-x(1);0 1 anchor_posi(2,7)-x(2);anchor_posi(1,7)-x(1) anchor_posi(2,7)-x(2) d7_observe^2+u(7)]>=0;
            [1 0 anchor_posi(1,8)-x(1);0 1 anchor_posi(2,8)-x(2);anchor_posi(1,8)-x(1) anchor_posi(2,8)-x(2) d8_observe^2+u(8)]>=0;
            
            [1 0 x(1);0 1 x(2);x(1) x(2) z]>=0;
            
            c(1)>=0;
            c(2)>=0;
            c(3)>=0;
            c(4)>=0;
            c(5)>=0;
            c(6)>=0;
            c(7)>=0;
            c(8)>=0;
            cvx_end;

%%%%%%%%%%%%%%%%%%%%%%%%%% end cvx %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

            x_estimated=x(1);y_estimated=x(2);              
            %final MSE calculation mse(real position, estimated position)
            mse_tmp = ((x_estimated - x_target(t_x))^2 + (y_estimated - y_target(t_y))^2)^0.5;
            mse_final = [mse_final mse_tmp];
            
            
        end
    end
end
mse_final_L=[mse_final_L;mse_final];

end
timestop = toc

mse_final_L_f=sum(mse_final_L)/L;

figure
plot(mse_final_L_f,’-.bo’);
legend (‘mse final’);
xlabel ‘target index’;
ylabel ‘MSE’;
title ‘MSE’

mcg · July 17, 2014, 10:52pm

It looks like a bug in either SeDuMi or the CVX/SeDuMi connector, or both. But honestly, this simply means that you should stick to using SDPT3! Each solver is going to have different performance characteristics, quirks, and yes, bugs.

kevin1 · July 18, 2014, 5:52pm

Thank you so much for your answer! I write this codes according to a paper, whose author used the CVX+SiDuMi to solve this problem. So this problem should be able to solved with cvx+sedumi.

mcg · July 18, 2014, 6:11pm

Well, certainly, you should, but there are myriad reasons why things can go wrong with an individual solver. Just stick with what works.