proposed revision of conic interface

[mlubin]

As discussed in #36, here's a proposed revision to the conic interface which allows the user to specify conic restrictions on both variables and affine functions of variables. Solver interfaces will be responsible for massaging the problem into the format required by each solver, but this interface makes it easier on the modeling side by avoiding the need for slacks and identity transformations.

The primal is:

min c'x
s.t. Ax - b in K_1
     x in K_2

and the dual is:

max b'y
s.t.   c - A'y in K_2^*
       y in K_1^*

The choice of signs for the affine constraints is arbitrary but results in a dual that's reasonably aesthetically pleasing to me (negative signs in the objective seem ugly).

Here's a preview of the docs: http://mathprogbasejl.readthedocs.org/en/conic2/conic.html

@madeleineudell @karanveerm @IainNZ @joehuchette

[IainNZ]

@madeleineudell @karanveerm you cool with this?

[madeleineudell]

Hi! Sorry for the long delay. Flipping the sign on the first constraint in
the primal problem to

min c'x
s.t.  b - Ax in K_1
       x in K_2

makes it look better to me; then the constraint is equivalent to $$Ax + s =
b$$ where the slack variable $$s \in K_1$$; and it's standard to have a
negative sign in the dual objective. But flipping the sign doesn't seem
particularly important. Other than that, the proposed interface looks
excellent.

On Tue, Sep 2, 2014 at 3:01 PM, Iain Dunning notifications@github.com
wrote:

@madeleineudell https://github.com/madeleineudell @karanveerm
https://github.com/karanveerm you cool with this?

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#38 (comment)
.

Madeleine Udell
PhD Candidate in Computational and Mathematical Engineering
Stanford University
www.stanford.edu/~udell

[mlubin]

Cool! I updated the signs as you suggested. I'll merge this soon.