ENH: linprog in SciPy 1.2+ discussion

scipy.optimize.linprog method='simplex' is in much better shape after several bug fixes and adopting the pre/postprocessing routines originally written for interior-point (closed #5400, #6139, #6690, #7044, #7237, #8174, and #8662 via PRs #8909, #8958, #9081, #9096, #9145 - thanks @kai-striega!). Essentially all known linprog bugs have been fixed. Consequently, it’s time for some enhancements!

To kick things off, I’ve submitted PR #9263 to add method = 'revised simplex'. The refactoring in #9145 paved the way for all linprog methods to share pre/postprocessing code, making it very easy to work this new method into the framework.

The fun is far from over, however. I opened this issue to record improvement ideas.

• use SuiteSparse in method = 'interior-point'when available
• allow user-specified linear solver (see gh-11201) (not important anymore; HiGHS linear solver is Fine)
• add sparse matrix support for method = 'revised simplex' (gh-12043 adds sparse simplex w/ HiGHS)
• for method='revised simplex', improve routine for driving artificial variables out of the basis by calculating only the required entries of the B^-1 A matrix, and update the basis matrix factorization rather than re-calculating from scratch (gh-12043 adds improved simplex)
• add an option to method = 'revised simplex' to perform the (revised) dual simplex method (and potentially include a heuristic for choosing between the two variants) (gh-12043 adds dual simplex)
• implement the Forest-Tomlin update for method='revised simplex' basis matrix factorization (gh-12043 has simplex with more efficient basis matrix updates)
• add a crossover routine (find basic feasible solution given a solution on the optimal face) for method = 'interior-point' (gh-12043 adds interior point with crossover)
• Add a basis-crashing routine for ‘method=revised simplex’ (solvers added by gh-12043 will have basis crashing evetually)
• include more sophisticated pivoting rules for method = 'revised simplex' (gh-12043 adds simplex with several pivoting rules)
• allow user to provide initial primal- or dual-feasible solution to method = 'revised simplex'
• add meaningful information about the dual of the original problem, especially for sensitivity analysis, to OptimizeResult produced for all methods (see gh-8836, gh-11848) (added marginals in gh-13893; still want ranging)
• add meaningful information about the standard form problem to OptimizeResult - along with details about the relationship between the standard form problem and the original problem (I don’t think this is important anymore.)
• add a routine for finding ALL basic optimal solutions to a given problem
• add functionality to aid in sensitivity analysis and updates to the linear programming problem (e.g. adding a constraint or changing a cost). For instance, the OptimizeResult object returned by linprog could include a copy of the standard form problem, solution vector, and any other information (basis, dual variables, etc.) to allow for a warm or hot start
• add tool for reading MPS files (I have code with nearly full functionality that could be cleaned up)
• add callback support for method = 'interior-point'/'revised simplex'
• improve the presolve routines: (HiGHS presolve is fine) - additional presolve techniques (see gh-9783), iterative resolve, sparse pivot-based redundancy removal, heuristics for pivot-based redundancy removal basis crashing, faster algorithm for redundancy removal (this would help), improve SVD method by removing multiple rows at a time when possible
• add automatic scaling routine (see gh-10495)
• add most Netlib benchmarks (see gh-10762)
• add redundancy removal benchmarks (see gh-10762)
• add support for integer constraints (I already have a fair amount of work done here that has been waiting for a reliable simplex solver, but there is quite a bit more to be done) (PR imminent)
• batch linear programming (#11195)

Please let me know if you are interested in any of these ideas and I’d be happy to share additional information.

[mdhaber]

Done. The important remaining items, colidated here for concision:

• add tool for reading MPS files (see gh-14593)
• add support for integer constraints (see mckib2/scipy#28, mckib2/scipy#31. SciPy PRs imminent.)
• add more advanced interface for exploring the problem and changes to the problem (see gh-14455. If HiGHS makes this sort of thing possible, we’ll eventually add it.)

[mdhaber]

Nice to meet you today, @melissawm!