Introduced relative KKT error data to HighsInfo, and using it to assess optimality claims from PDLP and IPM without crossover

[jajhall]

PDLP and IPM without crossover terminate with optimality using relative measures of KKT conditions. Hence it's unreasonable to expect the absolute KKT conditions used to determine optimality in simplex and IPM with crossover - when a basis is available. However, using measures of the bounds (costs) of the LP in relative measures of primal (dual) KKT conditions can flatter the solution obtained (particularly in the case of PDLP).

Hence, this PR introduces relative KKT error data - available to the user via HighsInfo - that are computed using the optimal solution, and ignore large costs and bounds that play no role in the optimal solution. The measures of the costs and bounds are computed for bounds that are active, and costs for which the corresponding dual is small.

The fix in #1978 to remove residual errors (that, previously, were not being checked for) after IPM without crossover by transferring them to primal and dual activities, was a bad idea. If nothing else, it led to a lot of erroneous model status values of HighsModelStatus::kUnknown when the problem had been solved satisfactorily using relative tolerances. This correction of residuals has now been removed. The relative residuals are assessed using the new measures. The large residuals that were reported, probably correspond to #2306

[codecov]

Codecov Report

Attention: Patch coverage is 83.07552% with 186 lines in your changes missing coverage. Please review.

Project coverage is 79.01%. Comparing base (c1e6903) to head (718829d).
Report is 165 commits behind head on latest.

Files with missing lines	Patch %	Lines
highs/lp_data/HighsInterface.cpp	55.98%	92 Missing ⚠️
highs/lp_data/HighsSolution.cpp	95.22%	23 Missing ⚠️
highs/lp_data/HighsModelUtils.cpp	0.00%	20 Missing ⚠️
highs/lp_data/Highs.cpp	77.77%	18 Missing ⚠️
highs/lp_data/HighsInfo.h	67.50%	13 Missing ⚠️
highs/pdlp/CupdlpWrapper.cpp	75.00%	8 Missing ⚠️
highs/ipm/IpxWrapper.cpp	20.00%	4 Missing ⚠️
check/TestPdlp.cpp	97.50%	2 Missing ⚠️
highs/lp_data/HighsOptions.h	86.66%	2 Missing ⚠️
highs/mip/HighsMipSolverData.cpp	0.00%	2 Missing ⚠️
... and 1 more

Additional details and impacted files

@@            Coverage Diff             @@
##           latest    #2346      +/-   ##
==========================================
- Coverage   79.08%   79.01%   -0.07%     
==========================================
  Files         346      346              
  Lines       84605    84969     +364     
==========================================
+ Hits        66906    67138     +232     
- Misses      17699    17831     +132     

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[jajhall]

The documentation of HighsOptions and HighsInfo has been updated to reflect the new options and data introduced.

FEATURES.md has been update with respect to recent merged PRs, and this PR!

[jajhall]

I've added @odow as a reviewer, mainly to flag up this significant change.

[odow]

If the Julia tests pass, I'm okay with it. We don't really have a good solver-independent way for users to check the quality of the returned solutions, but @joaquimg's tool that he is building should help.

[galabovaa]

Great!