```
K=4;
A =[ 24.0173 17.6637 78.0226 60.4402];
B =[ 156.1265 162.4801 102.1212 119.7036];
c=1.0000e-08*ones(1,4);
cvx_begin
variable tau0 nonnegative
tau1=1-tau0;
for i=1:K
R1=-rel_entr(tau1+ ((B(i)./c(i)) .* tau0 ), tau1+((B(i)+A(i))./c(i)) .* tau0 );
R2=-rel_entr( (B(i) ./ A(i)).*tau1 + (B(i)^2 ./( A(i).*c(i) ) ).*tau0, ...
(B(i) ./ A(i)).*tau1 + (B(i)^2 ./( A(i).*c(i) ) ).*tau0+ (B(i) ./ c(i)).*tau0) ;
R3=-rel_entr((B(i) ./ A(i)).*tau1 + (B(i)^2 ./( A(i).*c(i)) ).*tau0+ (B(i) ./ c(i)).*tau0,...
(B(i) ./ A(i)).*tau1 + (B(i)^2 ./( A(i).*c(i) ) ).*tau0) ;
end
maximize (R1+R2+R3);
subject to
tau0<=1;
cvx_solver mosek
cvx_end
```

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

mosek solver result is as follows.

## Calling Mosek 9.1.9: 38 variables, 13 equality constraints

For improved efficiency, Mosek is solving the dual problem.

MOSEK Version 9.1.9 (Build date: 2019-11-21 11:34:40)

Copyright © MOSEK ApS, Denmark. WWW: mosek.com

Platform: Windows/64-X86

MOSEK warning 62: The A matrix contains a large value of -1.6e+10 in constraint ‘’ (12) at variable ‘’ (2).

MOSEK warning 62: The A matrix contains a large value of -1.0e+11 in constraint ‘’ (12) at variable ‘’ (5).

MOSEK warning 62: The A matrix contains a large value of 4.3e+10 in constraint ‘’ (12) at variable ‘’ (7).

MOSEK warning 62: The A matrix contains a large value of -1.2e+11 in constraint ‘’ (12) at variable ‘’ (8).

MOSEK warning 62: The A matrix contains a large value of 3.7e+10 in constraint ‘’ (12) at variable ‘’ (10).

MOSEK warning 62: The A matrix contains a large value of -1.6e+10 in constraint ‘’ (12) at variable ‘’ (11).

MOSEK warning 62: The A matrix contains a large value of -1.5e+11 in constraint ‘’ (12) at variable ‘’ (14).

MOSEK warning 62: The A matrix contains a large value of 6.1e+10 in constraint ‘’ (12) at variable ‘’ (16).

MOSEK warning 62: The A matrix contains a large value of -1.7e+11 in constraint ‘’ (12) at variable ‘’ (17).

MOSEK warning 62: The A matrix contains a large value of 5.5e+10 in constraint ‘’ (12) at variable ‘’ (19).

Warning number 62 is disabled.

Problem

Name :

Objective sense : min

Type : CONIC (conic optimization problem)

Constraints : 13

Cones : 12

Scalar variables : 38

Matrix variables : 0

Integer variables : 0

Optimizer started.

Presolve started.

Linear dependency checker started.

Linear dependency checker terminated.

Eliminator started.

Freed constraints in eliminator : 0

Eliminator terminated.

Eliminator - tries : 1 time : 0.00

Lin. dep. - tries : 1 time : 0.01

Lin. dep. - number : 0

Presolve terminated. Time: 0.11

Problem

Name :

Objective sense : min

Type : CONIC (conic optimization problem)

Constraints : 13

Cones : 12

Scalar variables : 38

Matrix variables : 0

Integer variables : 0

Optimizer - threads : 4

Optimizer - solved problem : the primal

Optimizer - Constraints : 1

Optimizer - Cones : 12

Optimizer - Scalar variables : 38 conic : 36

Optimizer - Semi-definite variables: 0 scalarized : 0

Factor - setup time : 0.00 dense det. time : 0.00

Factor - ML order time : 0.00 GP order time : 0.00

Factor - nonzeros before factor : 1 after factor : 1

Factor - dense dim. : 0 flops : 5.30e+01

ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME

0 3.3e+00 2.7e+11 5.8e+01 0.00e+00 5.468532531e+01 -2.415306005e+00 1.0e+00 0.16

1 7.8e-01 6.5e+10 2.8e+01 -1.00e+00 3.623288422e+01 -1.764751023e+01 2.4e-01 0.39

2 2.4e-01 2.0e+10 1.6e+01 -1.00e+00 -2.023743658e+01 -6.457482339e+01 7.3e-02 0.39

3 2.6e-02 2.1e+09 5.1e+00 -1.00e+00 -7.557907627e+02 -6.856443070e+02 7.8e-03 0.41

4 8.8e-05 7.4e+06 3.0e-01 -1.00e+00 -2.408314867e+05 -2.035103403e+05 2.7e-05 0.41

5 1.5e-10 1.3e+01 3.3e-04 -1.00e+00 -9.698071853e+10 -8.193276523e+10 4.7e-11 0.42

Optimizer terminated. Time: 0.63

Interior-point solution summary

Problem status : DUAL_INFEASIBLE

Solution status : DUAL_INFEASIBLE_CER

Primal. obj: -6.4447685340e+00 nrm: 6e+00 Viol. con: 4e+01 var: 6e+00 cones: 2e-11

Optimizer summary

Optimizer - time: 0.63

Interior-point - iterations : 5 time: 0.42

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

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

And sedumi solver result is as follows.

## Successive approximation method to be employed.

For improved efficiency, SeDuMi is solving the dual problem.

SeDuMi will be called several times to refine the solution.

Original size: 38 variables, 13 equality constraints

12 exponentials add 96 variables, 60 equality constraints

## Cones | Errors |

Mov/Act | Centering Exp cone Poly cone | Status

--------±--------------------------------±--------

0/ 1 | 8.000e+00 5.373e+06 5.373e+06 | Failed

0/ 1 | 8.000e+00 3.909e+08 3.909e+08 | Failed

0/ 1 | 8.000e+00 6.995e+07 6.995e+07 | Failed

Status: Failed

Optimal value (cvx_optval): NaN

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Both solver failed to solve.