Clarification on lcons/ucons/sense in OptimizationProblem documentation

[DanielVandH]

What are lcons and ucons in the definition of an OptimizationProblem? The documentation says:

lcons and ucons are the upper and lower bounds for equality constraints on the optimization. They should be an AbstractArray matching the geometry of u, where (lcons[I],ucons[I]) is the constraint (lower and upper bounds) for cons[I].

But in OptimizationProblem, this cons vector seems to take the form res = cons(x, p) and the constranits are satisfied when res = 0 - where do the lower and upper bounds come in here? Maybe it would be useful to have a clear mathematical representation of an optimisation problem that lays this out, e.g (a LaTeXed version of?)

minimise f(u, p)
subject to lb[i] <= u[i] <= ub[i], i in eachindex(u)
lb[I] <= cons(u, p)[I] <= ucons[I], i in eachindex(u),

assuming that the latter is what lcons/ucons is actually supposed to represent.

Also just on the problem of this OptimizationProblem documentation, the sense keyword is not defined in this documentation (actually, lcons/ucons/sense are the only fields left blank at the bottom), and the objective function at the start of the documentation I imagine is supposed to be just $$\min_u f(u, p)$$ rather than $\min_u f(u, p) = 0$.

[ChrisRackauckas]

lcons and ucons are upper and lower bounds for the box of the constraints, while cons is for the equations to be satisfied. @Vaibhavdixit02 can you fill in how you see that being used for the inequality and equality constraints? I left that blank for now because I didn't think it was completed.

the sense keyword is not defined in this documentation

I'm not sure that ever got finished being implemented, so it's purposefully not documented until it's usable.

[gaurav-arya]

I'm also having trouble interpreting the docs. An OptimizationFunction accepts the kwarg:

cons(res,x,p) or res=cons(x,p): the equality constraints vector, where the constraints are satisfied when res = 0.

There are then a couple more kwargs, provided to the OptimizationProblem:

lcons and ucons are the upper and lower bounds for equality constraints on the optimization. They should be an AbstractArray matching the geometry of u, where (lcons[I],ucons[I]) is the constraint (lower and upper bounds) for cons[I].

The sentence "upper and lower bounds for equality constraints" doesn't make sense to me. My best guess is that cons simply represents the function that produces the LHS of the constraints, agnostic to whether they are inequality/equality constraints. If they are indeed inequality constraints, the bounds can be specified in the OptimizationProblem via lcons and ucons, while by default (?) they are equality constraints res = 0.

Is this the right interpretation?

[ChrisRackauckas]

Default is inf.

@Vaibhavdixit02 it's been almost a month now. Either the docs need to be finished here and the guardrails need to be added (i.e. error on solvers not supporting constraints), or we should add a warning to the docs that cons is unfinished right now. It was merged on the premise that these parts would be completed ASAP but it's starting to drag on and it's not a good look.