H=50;Vmax=20;z=10;T=5;N=20;t=T/N;I=4;t0=t/I;B=40*10^6;Z=10;c=0.5*Z*t;
o2=10^-9;om2=10^-13;
y0=10^-6;
c1=1000;c2=1000;c3=1000;c4=1000;ci=[c1,c2,c3,c4];
cm1=1000;cm2=1000;cm3=1000;cm4=1000;cmi=[cm1,cm2,cm3,cm4];
I1=45*10^6;I2=48*10^6;I3=50*10^6;I4=52*10^6;Ii=[I1,I2,I3,I4];
Im1=45*10^6;Im2=48*10^6;Im3=50*10^6;Im4=52*10^6;Imi=[Im1,Im2,Im3,Im4];
ku=10^-28;ki=10^-28;kmi=10^-28;
s1=[5;5];s2=[5;-5];s3=[-5;-5];s4=[-5;5];si=[s1,s2,s3,s4];
sm1=[20;20];sm2=[20;-20];sm3=[-20;-20];sm4=[-20;20];smi=[sm1,sm2,sm3,sm4];
u0=[[-10;0],[-8;0],[-6;0],[-4;0],[-2;0],[0;0],[2;0],[4;0],[6;0],[8;0],[6;0],[4;0],[2;0],[0;0],[-2;0],[-4;0],[-6;0],[-8;0],[-10;0],[-10;0]];
q0=[-10;0];qF=q0;
hm1=(10^-2)*y0*(norm(si(:,1)-smi(:,1)))^-4;hm2=(10^-2)*y0*(norm(si(:,2)-smi(:,2)))^-4;hm3=(10^-2)*y0*(norm(si(:,3)-smi(:,3)))^-4;hm4=(10^-2)*y0*(norm(si(:,4)-smi(:,4)))^-4;
hmi=[hm1,hm2,hm3,hm4];hmi=repmat(hmi,N,1);
cvx_begin
cvx_solver sedumi
cvx_precision best
variables fi(N,I) fmi(N,I) fiu(N,I) fmiu(N,I);
variables lmilo(N,I) lioff(N,I) lilo(N,I);
expression pmilo(N,I);
expression pioff(N,I);
expression pilo(N,I);
expression hi(N,I);
expression sum21(N,I);
expression sum22(N,I);
expression sum31(N,I);
expression sum32(N,I);
expression sum4_i(I);
expression sum4_uav(I);
expression sum5_i(I);
expression sum5_uav(I);
expression sum6(I);
expression sum7(I);
for i=1:I
for n=1:N
pmilo(n,i)=om2*(2^(lmilo(n,i)/(B*t0))-1)/hmi(n,i);
end
end
for i=1:I
for n=1:N
hi(n,i)=y0/(H^2+(norm(u0(:,n)-si(:,i)))^2);
pioff(n,i)=o2*(2^(lioff(n,i)/(B*t0))-1)/hi(n,i);
end
end
for i=1:I
for n=1:N
hi(n,i)=y0/(H^2+(norm(u0(:,n)-si(:,i)))^2);
pilo(n,i)=o2*(2^(lilo(n,i)/(B*t0))-1)/hi(n,i);
end
end
minimize(sum(sum(t*ki*pow_p(fi,3)))+sum(sum(t*kmi*pow_p(fmi,3)))+sum(sum(t*ku*pow_p(fiu,3)))+sum(sum(t*ku*pow_p(fmiu,3)))+...
+sum(sum(t0*pmilo))+sum(sum(t0*pioff))+sum(sum(t0*pilo)))
subject to:
sum21(1,1)=0;sum21(1,2)=0;sum21(1,3)=0;sum21(1,4)=0;sum22(1,1)=0;sum22(1,2)=0;sum22(1,3)=0;sum22(1,4)=0;
sum31(1,1)=0;sum31(1,2)=0;sum31(1,3)=0;sum31(1,4)=0;sum32(1,1)=0;sum32(1,2)=0;sum32(1,3)=0;sum32(1,4)=0;
for i=1:I
for n=1:N
lmilo(n,i)<=lioff(n,i);
end
end
for i=1:I
for k=2:N
sum21(k,i)=0;sum22(k,i)=0;
for n=2:k
sum21(k,i)=sum21(k,i)+lilo(n,i);
E2=t*fiu(n,i)/ci(i);
sum22(k,i)=sum22(k,i)+E2;
end
sum21(k,i)+lilo(1,i)-lilo(k,i)>=sum22(k,i);
end
end
for i=1:I
for k=2:N
sum31(k,i)=0;sum32(k,i)=0;
for n=2:k
sum31(k,i)=sum31(k,i)+lioff(n,i);
E3=t*fmiu(n,i)/cmi(i);
sum32(k,i)=sum32(k,i)+E3;
end
sum31(k,i)+lioff(1,i)-lioff(k,i)>=sum32(k,i);
end
end
for i=1:I
sum4_i(i)=0;sum4_uav(i)=0;
for n=1:N
sum4_i(i)=sum4_i(i)+lilo(n,i);
sum4_uav(i)=sum4_uav(i)+t*fiu(n,i)/ci(i);
end
sum4_i(i)==sum4_uav(i);
end
for i=1:I
sum5_i(i)=0;sum5_uav(i)=0;
for n=1:N
sum5_i(i)=sum5_i(i)+lioff(n,i);
sum5_uav(i)=sum5_uav(i)+t*fmiu(n,i)/cmi(i);
end
sum5_i(i)==sum5_uav(i);
end
for i=1:I
sum6(i)=0;
for n=1:N
L6=t*fmi(n,i)/cmi(i)+lmilo(n,i);
sum6(i)=sum6(i)+L6;
end
sum6(i)==Imi(i);
end
for i=1:I
sum7(i)=0;
for n=1:N
L7=t*fi(n,i)/ci(i)+lilo(n,i);
sum7(i)=sum7(i)+L7;
end
sum7(i)==Ii(i);
end
for i=1:I
lmilo(N,i)==0,lioff(N,i)==0,lilo(N,i)==0,fiu(1,i)==0;fmiu(1,i)==0;
end
0<=fi;0<=fmi;0<=fiu;0<=fmiu;0<=lmilo;0<=lioff;0<=lilo;
cvx_end
The result of running under different solvers is
sedumi:
For improved efficiency, SeDuMi is solving the dual problem.
SeDuMi will be called several times to refine the solution.
Original size: 3448 variables, 1420 equality constraints
240 exponentials add 1920 variables, 1200 equality constraints
-----------------------------------------------------------------
Cones | Errors |
Mov/Act | Centering Exp cone Poly cone | Status
--------+---------------------------------+---------
0/ 0 | 0.000e+00 0.000e+00 0.000e+00 | Unbounded
0/ 0 | 0.000e+00 0.000e+00 0.000e+00 | Unbounded
0/ 0 | 0.000e+00 0.000e+00 0.000e+00 | Unbounded
-----------------------------------------------------------------
Status: Infeasible
Optimal value (cvx_optval): +Inf
sdpt3:
For improved efficiency, SDPT3 is solving the dual problem.
SDPT3 will be called several times to refine the solution.
Original size: 3448 variables, 1420 equality constraints
240 exponentials add 1920 variables, 1200 equality constraints
-----------------------------------------------------------------
Cones | Errors |
Mov/Act | Centering Exp cone Poly cone | Status
--------+---------------------------------+---------
0/240 | 3.500e+00 9.107e-12 9.106e-12 | Failed
0/240 | 1.750e+00 9.107e-12 0.000e+00 | Failed
0/240 | 8.750e-01 9.106e-12 0.000e+00 | Failed
-----------------------------------------------------------------
Status: Failed
Optimal value (cvx_optval): NaN
mosek:
MOSEK Version 9.1.9 (Build date: 2019-11-21 11:34:40)
Copyright (c) MOSEK ApS, Denmark. WWW: mosek.com
Platform: Windows/64-X86
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 1420
Cones : 880
Scalar variables : 3448
Matrix variables : 0
Integer variables : 0
Optimizer started.
Presolve started.
Linear dependency checker started.
Linear dependency checker terminated.
Eliminator started.
Freed constraints in eliminator : 312
Eliminator terminated.
Eliminator started.
Freed constraints in eliminator : 0
Eliminator terminated.
Eliminator - tries : 2 time : 0.00
Lin. dep. - tries : 1 time : 0.00
Lin. dep. - number : 0
Presolve terminated. Time: 0.02
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 1420
Cones : 880
Scalar variables : 3448
Matrix variables : 0
Integer variables : 0
Optimizer - threads : 16
Optimizer - solved problem : the dual
Optimizer - Constraints : 1096
Optimizer - Cones : 872
Optimizer - Scalar variables : 3072 conic : 2616
Optimizer - Semi-definite variables: 0 scalarized : 0
Factor - setup time : 0.01 dense det. time : 0.00
Factor - ML order time : 0.00 GP order time : 0.00
Factor - nonzeros before factor : 9560 after factor : 1.03e+04
Factor - dense dim. : 0 flops : 2.99e+05
ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME
0 1.2e+00 5.2e+07 5.5e+02 0.00e+00 5.052244804e+02 -4.645145178e+01 1.0e+00 0.05
1 3.5e-01 1.6e+07 3.0e+02 -1.00e+00 4.189844956e+02 -1.303625096e+02 3.0e-01 0.13
2 9.7e-02 4.3e+06 1.6e+02 -1.00e+00 1.096225810e+02 -4.310461421e+02 8.3e-02 0.13
3 1.8e-02 7.9e+05 6.8e+01 -1.00e+00 -1.775086595e+03 -2.261889257e+03 1.5e-02 0.13
Optimizer terminated. Time: 0.14
Interior-point solution summary
Problem status : DUAL_INFEASIBLE
Solution status : DUAL_INFEASIBLE_CER
Primal. obj: -2.6946830750e+01 nrm: 5e+02 Viol. con: 2e-13 var: 0e+00 cones: 9e-03
Optimizer summary
Optimizer - time: 0.14
Interior-point - iterations : 3 time: 0.13
Basis identification - time: 0.00
Primal - iterations : 0 time: 0.00
Dual - iterations : 0 time: 0.00
Clean primal - iterations : 0 time: 0.00
Clean dual - iterations : 0 time: 0.00
Simplex - time: 0.00
Primal simplex - iterations : 0 time: 0.00
Dual simplex - iterations : 0 time: 0.00
Mixed integer - relaxations: 0 time: 0.00
------------------------------------------------------------
Status: Infeasible
Optimal value (cvx_optval): +Inf
If I remove the target, there are two solvers that work