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

AI-Use Disclosure

• AI tools were NOT used during the preparation of this PR

or

• AI tools contributed to the development of this PR

  • AI tools generated documentation (including the PR description/comments, code comments, and/or Sphinx documentation)
  • AI tools generated tests (baselines, examples, and/or code)
  • AI tools generated code (apart from tests)

  Review process (select ONE):

  • Rewritten: All AI-generated content was rewritten by me before being committed.
  • Reviewed/verified: I retained AI-generated content and verified it before committing. Verification included (as applicable):
    • Ran the code and fixed issues
    • Added and ran tests
    • Checked correctness/logic of code and tests
    • Checked for alignment with the contribution guide
    • Considered security implications
  • As-is: AI-generated content was commited directly to the repository

Notes for reviewers (optional):

Legal Acknowledgement

By contributing to this software project, I have read the contribution guide and agree to the following terms and conditions for my contribution:

1. I agree my contributions are submitted under the BSD license.
2. I represent I am authorized to make the contributions and grant the license. If my employer has rights to intellectual property that includes these contributions, I represent that I have received permission to make contributions and grant the required license on behalf of that employer.

[stephenscini]

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