Update ParOpt interface to support sparse constraints

[A-CGray]

Purpose

ParOpt now supports sparse constraints which should help some of the performance issues I've run into with it for problems with a lot of constraints.

To use this functionality, the ParOpt problem you create needs to define new methods for computing the sparse constraints separately and another for computing jac-vec products with the sparse constraint jacobian.

As a first step, I figured the best approach would be to treat the linear constraints as sparse and the nonlinear constraints as dense.

I'm opening this as a draft now as I'm not sure the best way to separate the evaluation of the linear and nonlinear constraints, hoping to get @ewu63 's opinion. In particular, I think ParOpt will call the jac-vec product function quite a lot so it might be important to make that quite efficient, ideally we would just have a single sparse mat for all the linear constraints and then do a single mat-vec product.

Closes #353

Expected time until merged

Type of change

• Bugfix (non-breaking change which fixes an issue)
• New feature (non-breaking change which adds functionality)
• Breaking change (non-backwards-compatible fix or feature)
• Code style update (formatting, renaming)
• Refactoring (no functional changes, no API changes)
• Documentation update
• Maintenance update
• Other (please describe)

Testing

Checklist

• I have run flake8 and black to make sure the Python code adheres to PEP-8 and is consistently formatted
• I have formatted the Fortran code with fprettify or C/C++ code with clang-format as applicable
• I have run unit and regression tests which pass locally with my changes
• I have added new tests that prove my fix is effective or that my feature works
• I have added necessary documentation

[A-CGray]

@gjkennedy just tagging to make you aware of this

[codecov]

Codecov Report

Attention: Patch coverage is 50.00000% with 2 lines in your changes missing coverage. Please review.

Project coverage is 74.89%. Comparing base (bc021e4) to head (9011d96).

Files with missing lines	Patch %	Lines
pyoptsparse/pyParOpt/ParOpt.py	50.00%	2 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #409      +/-   ##
==========================================
- Coverage   74.92%   74.89%   -0.03%     
==========================================
  Files          22       22              
  Lines        3334     3338       +4     
==========================================
+ Hits         2498     2500       +2     
- Misses        836      838       +2     

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[A-CGray]

@gjkennedy I see there are two different ways to work with sparse constraints in ParOpt:

1. Implement evalSparseObjCon and evalSparseObjConGradient so that the sparse constraints and jacobian are returned along with the dense constraints
2. Implement separate evalSparseCon and addSparseJacobian methods just for evaluating the sparse constraints.

Is either one of these approaches preferable from ParOpt's point of view? Also, in option 1 I see that evalSparseObjConGradient directly populates the data array of the ParOpt sparse jacobian, how/when is the sparsity pattern supposed to be given to ParOpt?

[A-CGray]

Closing as this is superceded by #414