[Depends on #3991] Adding method for multistart initialization of nonlinear models.

[stephenscini]

Fixes # .

Summary/Motivation:

Additional method in devel/initialization to use multistart optimization as a way for initializing nonliner models.

Changes proposed in this PR:

• Updating contrib/multistart solver for reproducibility, and adding support for new solver interface.
• Adding support for uniform, lhs, and sobol sampling within the multistart solver
• Adding method to devel/initialization

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[stephenscini]

Opening PR, but still in active development. Dependent on #3991 first as it includes those changes.

[stephenscini]

Note for 7/21 Dev meeting

Method implemented with support for new solver interface. All original tests passing locally.

Tasks before ready for review:

• It looks like there is an issue with changing the SolverFactory version in a different place, which I will address.
• Try and simplify interface, check with mentors.
• Add tests for new functionality

[stephenscini]

Went through and added some questions in the code for design meeting.

[stephenscini]

I received an error message when I added the solver to the new SolverFactory that it needed to be in this list. This would mean it is tested with the other solvers from contrib/solver and I am not sure that if that is expected? If so, will all contrib solvers need to eventually be switched over or should the opt/solvers still be the best location.

In this case, I wanted to update it to use these solvers so thought it would also go here. Maybe Legacy?

[stephenscini]

Could/should this also support a user supplying a list of initial points? Thinking of obj_at_theta in parmest. Goal in my head is to make as generalized as possible.

[stephenscini]

Had discussion with Bethany and Michael. Main takeaway points:

• Invest to make this work for newer SolverFactory. Do not keep in opt.SolverFactory.
• Try and resolve all test failures with the new SolverFactory as default. More discussion needed on expectations for contrib solvers as they transition to new SolverFactory.
• If all results are infeasible/not optimal, have it throw the 'NoOptimalSolution' error.
  -Keep this PR focused on a minimum working version that has key functionality we want. Can always add additional touches later.
• LHS makes sense to be default for all methods/strategies, and should be looped in to the old strategies too.
• Availability of multistart should depend on availablility of chosen sub-solver (default is ipopt)
• Version 0.1.0 makes sense for this new iteration.
• Subsolver has its own configuration, but still needs to comply with 'meta-solver' configurations. If subsolver timelimit is 1 minute for 50 runs, but metasolver is 10 minutes, when metasolver time runs out the methods stop.