How can we solve the sum of squares programming problem with linear fractional function as the objective function ?

[SUZI]

Hi, all

I'm solving a SOSP with linear fractional function as the objective function, but mosek says "Solver not applicable (mosek does not support semidefinite constraints)".

So, how can we solve the sum of squares programming problem with linear fractional function as the objective function ?

Thank you!

[Johan Löfberg]

you would have to do bisection, i.e. replace g(x)/f(x) with g(x) <= f(x)*t and then perform bisection of t

the error message is weird though as mosek supports SDPs, so you would have to supply a reproducible example to illustrate that

[SUZI]

Dear Johan

Thanks for your reply. this is my code.

[Johan Löfberg]

You've got some signomial stuff in the model, hence Mosek is not applicable on the resulting nonlinear SDP

>> constrains
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
|    ID|                                Constraint|   Coefficient range|
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
|    #1|     Sum-of-square constraint (polynomial)|                    |
|    #2|     Sum-of-square constraint (polynomial)|                    |
|    #3|     Sum-of-square constraint (polynomial)|                    |
|    #4|     Sum-of-square constraint (polynomial)|                    |
|    #5|   Element-wise inequality (sigmonial) 1x1|              1 to 1|
|    #6|     Sum-of-square constraint (polynomial)|                    |
|    #7|     Sum-of-square constraint (polynomial)|                    |
|    #8|     Sum-of-square constraint (polynomial)|                    |
|    #9|     Sum-of-square constraint (polynomial)|                    |
|   #10|     Sum-of-square constraint (polynomial)|                    |
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

[SUZI]

The previous expression at line 46 was c_m1(1)/c_m2(1)>=1, and now changed to c_m1(1)>=c_m2(1).

the following is the Constraint|   Coefficient range.

but it still display "Solver not applicable (mosek does not support semidefinite constraints)"

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
|    ID|                              Constraint|   Coefficient range|

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
|    #1|   Sum-of-square constraint (polynomial)|                    |
|    #2|   Sum-of-square constraint (polynomial)|                    |
|    #3|   Sum-of-square constraint (polynomial)|                    |
|    #4|   Sum-of-square constraint (polynomial)|                    |

|    #5|             Element-wise inequality 1x1|              1 to 1|

|    #6|   Sum-of-square constraint (polynomial)|                    |
|    #7|   Sum-of-square constraint (polynomial)|                    |
|    #8|   Sum-of-square constraint (polynomial)|                    |
|    #9|   Sum-of-square constraint (polynomial)|                    |
|   #10|   Sum-of-square constraint (polynomial)|                    |
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

[Johan Löfberg]

you still have the same issue in the objective

[SUZI]

ok, thanks

and in the following picture,  are you saying I should use the Dinkelbach’s algorithm?

[Johan Löfberg]

I am not advocating or talking about any specialized strategy, but just that the obvious (not necessarily fast, good or necessary) hack is to bisect

https://yalmip.github.io/command/bisection/

https://yalmip.github.io/example/decayrate/

[SUZI]

ok, thanks for your help