QP ASM: zero-sized Cholesky storage causes NaNs and a false Unbounded status #3453

Please provide the following information where possible/relevant and check out CONTRIBUTING.md.

What version of HiGHS and what language are you using?
Version: v1.15.1
Language: C++. The issue was originally observed through Python and independently reproduced with a standalone C++ replay.

Which solver are you using (e.g. LP, MIP, QP)

QP active-set solver (QP ASM).

What operating system (Linux, Windows, ...) and version?

Windows x64, MSVC 19.41.34123.0.

What did you do?
Steps to reproduce the behaviour:

1. Build unmodified HiGHS at latest commit in master brance in Release mode.
2. Build the supplied highs_qp_replay.cpp against HiGHS, with highs_case_data.h in the same directory.
3. Run qp_replay.exe 0.

What did you expect to see

An Optimal status with a finite solution.

What did you see instead?

HiGHS returned Unbounded after 76 QP iterations. The returned primal solution contained NaNs at zero-based variable indices 11 and 17.

Make sure you include information that can help us debug (full error message, model if possible).

Anything else we should know about your project / environment

The problem appears to originate in highs/qpsolver/factor.hpp:

• recompute() resizes the Cholesky storage to zero when the null-space dimension is zero.
• Subsequent expand() doubles that storage dimension, which remains zero.
• The code then accesses an empty vector with a zero matrix stride, corrupting the factor and eventually producing Inf/NaN.

Locally, keeping the storage dimension at least one in resize() resolves this failure without changing the actual null-space dimension:
new_k_max = max(HighsInt(1), new_k_max);

With this change, the same QP returns Optimal with finite values and a maximum constraint violation of approximately 3.55e-14.

A two-variable regression fails without the fix and passes with it. All 21 QP tests pass in Release and Debug, and the full Release CTest suite passes 165/165 tests.

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highs-zero-cholesky-repro.zip