Imposition of dual exponential cone constraints

[Pantelis Sopasakis]

I would like to impose dual exponential constraints on some variables. 

The dual exponential cone is defined as

Ked={(u,v,w)∈R3:u≤0,w≥0,−ulog(−uw)+u−v≤0}

with the convention 0*log(0/w) = 0 for all w>=0.

I would like to impose the constraint y in K^{ed}.

I tried with kullbackleibler and required that w>=1e-8 and u<=1e-8. 

What is more, YALMIP complains that MOSEK is not an appropriate solver, whereas such constraints are supported by MOSEK.

Any suggestions?

[Johan Löfberg]

mosek does not support exponential cones in the public release yet (and thus yalmip does not support it via mosek yet. It's in the pipe-line though)

dual exponential cone is not supported at all (as a special object), exponential cone is supported in yalmip via ecos and scs (and of course as any other nonlinearity in general nonlinear solvers)

[Erling D. Andersen]

MOSEK v9 should support the dual exponential cone.

Also using a simple linear transformation you can map the dual cone to the primal cone. In other words s slight reformulation makes it possible to use the primal cone instead of the dual.

[Pantelis Sopasakis]

Dear Erling and Johan, thank you for your answers. 

I tried with SCS and it works fine. I'm using MOSEK 8.

I wanted to make an optimizer instead of using optimize, but it seems it isn't possible.

I get the following error message:

Error using optimizer (line 303)
Parameters are currently only allowed to enter function such as exp, sin etc as exp(a), sin(b) etc.

[Johan Löfberg]

you can get around that limitation by replacing exp(expression_of_parameters_and_decisionvariables) with a new variable z, use exp(z) and add the constraint z == expression_of_parameters_and_decisionvariables