test that ConstraintPrimal returns exact value of function at result point (not set constant)

[chriscoey]

see http://www.juliaopt.org/MathOptInterface.jl/dev/apireference/#MathOptInterface.ConstraintPrimal

this would help detect issues like jump-dev/ECOS.jl#81

the test should check (exact) equality, not approximate equality

[mlubin]

Checking for exact equality is inconsistent with solvers that have separate values to represent the constraint primal. e.g., conic solvers where b - Ax in C is reformulated as s = b - Ax, s in C. ConstraintPrimal should return s in this case.

[chriscoey]

from the definition:

Given a constraint function-in-set, the ConstraintPrimal is the value of the function evaluated at the primal solution of the variables

to me that suggests returning b - Ax not s

[mlubin]

Then we need to tweak the definition. The intention was what I just wrote.

[chriscoey]

do you have any example use cases? why did you decide s instead of b - Ax for solvers that require slacks?

[chriscoey]

and is there a plan to have a bridge that converts non-slack constraints to equalities and slack constraints?

[mlubin]

SCS's solution is described by (x*, s*, y*) where x is the primal, s is the slacks, and y is the duals (https://github.com/cvxgrp/scs). If we map ConstraintPrimal and ConstraintPrimalStart to s then we can round-trip between an optimal SCS solution and an optimal starting point with no loss of information.

[mlubin]

and is there a plan to have a bridge that converts non-slack constraints to equalities and slack constraints?

Probably, not sure

[blegat]

Yes it is planned #528

[odow]

I'm not entirely sure how we would test this. Perhaps we just need to update the documentation to mention the slacks?