fix and extend tests for conic duals

[mlubin]

CC @madeleineudell @kaarthiksundar @IainNZ @joehuchette

[mlubin]

CC @ulfworsoe

[IainNZ]

Looks good on phone. I could have sworn we sanity checked the signs on these

[ulfworsoe]

Ok... I am probably misunderstanding something. What is your definition of
the dual sets?

Using the model from
http://mathprogbasejl.readthedocs.org/en/latest/conic.html

S = { x > 0 }, S* = { s > 0 }
S = { x < 0 }, S* = { s < 0 }
S = { x = 0 }, S* = { s unbounded }
S = { x1^2 < x2^2 + ... + xn^2 }, S* = { x < 0 } , S* = { s1^2 < s2^2 + ...

• sn^2 }
  S = Positive semidefinite, S* = Positive Semidefinite

Is this correct?

On Tue, Aug 11, 2015 at 3:20 PM, Iain Dunning notifications@github.com
wrote:

Looks good on phone. I could have sworn we sanity checked the signs on
these

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#82 (comment)
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Ulf Worsøe
Mosek ApS

ulf.worsoe@mosek.com
www.mosek.com

[mlubin]

@ulfworsoe, yes, NonNeg, NonPos, SOC, and SDP are self dual.

[ulfworsoe]

Now I am just being stupid. Doesn't this test
https://github.com/JuliaOpt/MathProgBase.jl/blob/master/test/conicinterface.jl#L206
check if the root of the dual SOC cone is negative?

On Tue, Aug 11, 2015 at 4:12 PM, Miles Lubin notifications@github.com
wrote:

@ulfworsoe https://github.com/ulfworsoe, yes, NonNeg, NonPos, SOC, and
SDP are self dual.

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#82 (comment)
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Ulf Worsøe
Mosek ApS

ulf.worsoe@mosek.com
www.mosek.com

[mlubin]

@ulfworsoe, yes, but that should be fixed in this PR

[mlubin]

Let me know if anyone finds something off here, otherwise I'll merge and tag so we can get to fixing the solvers.

[bodono]

👍