Lmin1 = 1e5;
Lmin2 = Lnin2;
Emax1 = 1;
Emax2 = Emax1;
T_max = 1;
em1 =10^(-28);
em2 = em1;
Cm1 =1000;
Cm2 = 1000;
eta = 0.1;
cvx_begin
variable fm1;
variable fm2;
expression r_opt1;
r_opt1=((T_max * fm1)/Cm1+(T_max * fm2)/Cm2-eta
* (em1 * pow_p(fm1,3) * T_max+em2 * pow_p(fm2,3) * T_max));
maximize (r_opt1);
subject to
r_opt1>=0;
em1 * pow_p(fm1,3) * T_max<=Emax1;
em2 * pow_p(fm1,3) * T_max<=Emax2;
(T_maxfm1)/Cm1>=Lmin1;
(T_maxfm2)/Cm2>=Lmin2;
cvx_end
EE = ((T_max * fm1)/Cm1+(T_max * fm2)/Cm2)/
(em1 * pow_p(fm1,3) * T_max+em2 * pow_p(fm2,3) * T_max));
Calling Mosek 9.1.9: 29 variables, 10 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 710: #1 (nearly) zero elements are specified in sparse col ‘’ (1) of matrix ‘A’.
MOSEK warning 710: #1 (nearly) zero elements are specified in sparse col ‘’ (2) of matrix ‘A’.
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 10
Cones : 8
Scalar variables : 29
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 started.
Freed constraints in eliminator : 0
Eliminator terminated.
Eliminator - tries : 2 time : 0.00
Lin. dep. - tries : 1 time : 0.02
Lin. dep. - number : 0
Presolve terminated. Time: 0.02
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 10
Cones : 8
Scalar variables : 29
Matrix variables : 0
Integer variables : 0
Optimizer - threads : 8
Optimizer - solved problem : the primal
Optimizer - Constraints : 6
Optimizer - Cones : 8
Optimizer - Scalar variables : 27 conic : 24
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 : 11 after factor : 11
Factor - dense dim. : 0 flops : 1.23e+02
ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME
0 1.0e+00 5.5e+08 5.0e+00 0.00e+00 4.000000000e+00 0.000000000e+00 1.0e+00 0.03
1 1.9e-01 1.0e+08 2.2e+00 -1.00e+00 -3.171390333e-01 1.149462981e-11 1.9e-01 0.08
2 2.2e-02 1.2e+07 7.4e-01 -1.00e+00 -4.125160478e+01 3.144677845e-11 2.2e-02 0.08
3 4.3e-03 2.4e+06 1.1e+00 -1.00e+00 -2.158197645e+02 5.926207086e-11 4.3e-03 0.09
4 4.2e-04 2.3e+05 1.8e-01 -1.00e+00 -2.398504135e+03 1.214997294e-10 4.2e-04 0.09
5 2.1e-04 1.1e+05 1.3e-01 -1.00e+00 -4.820043246e+03 1.785122580e-10 2.1e-04 0.09
6 6.4e-05 3.5e+04 7.1e-02 -1.00e+00 -1.552158857e+04 1.052654549e-10 6.4e-05 0.09
7 1.2e-05 6.5e+03 3.0e-02 -1.00e+00 -8.461762521e+04 2.345142750e-10 1.2e-05 0.09
8 2.3e-06 1.2e+03 1.3e-02 -1.00e+00 -4.443833441e+05 7.334770817e-10 2.3e-06 0.11
9 4.2e-07 2.3e+02 5.7e-03 -1.00e+00 -2.409991557e+06 1.393833977e-09 4.2e-07 0.11
10 5.2e-08 2.8e+01 2.0e-03 -1.01e+00 -2.017783630e+07 2.104659796e-09 5.2e-08 0.11
11 1.2e-08 6.7e+00 1.0e-03 -1.06e+00 -9.641735492e+07 3.714037225e-09 1.2e-08 0.11
Optimizer terminated. Time: 0.13
Interior-point solution summary
Problem status : DUAL_INFEASIBLE
Solution status : DUAL_INFEASIBLE_CER
Primal. obj: -1.0509320264e+00 nrm: 7e+08 Viol. con: 4e-08 var: 0e+00 cones: 8e-09
Optimizer summary
Optimizer - time: 0.13
Interior-point - iterations : 11 time: 0.11
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