feat: Add relax() and unrelax() to Variable and Variables

[FBumann]

Follow up on #625

Summary

• Adds relax() / unrelax() / relaxed to Variable and Variables, enabling LP relaxation of MILP models
• Supports partial relaxation via filtered views: m.variables.integers.relax(), m.variables.binaries.relax(), or individual m.variables["x"].relax()
• Semi-continuous variables raise NotImplementedError (their LP relaxation requires bound changes, not just a flag flip)
• Removes the relax parameter from fix() — the canonical workflow is now fix() then relax() as separate, composable operations

Usage

# Full LP relaxation
m.variables.relax()
m.solve()
m.variables.unrelax()

# Relax only integers, keep binaries as-is
m.variables.integers.relax()
m.solve()
m.variables.unrelax()

# Relax a single variable
m.variables["z"].relax()

# Fix-then-relax for MILP dual extraction
m.variables.fix()
m.variables.relax()
m.solve()
m.constraints["con1"].dual

# Fix a subset of variables to explore the feasible space
m.variables["commitment"].fix()
m.solve()

This is sort of a refactor of #625 which works fine as not released yet!

Test plan

• Tests for Variable.relax() / unrelax() on binary, integer, continuous, and semi-continuous
• Tests for Variables.relax() / unrelax() on full and filtered containers
• Tests for combined fix+relax workflow and unfix restoring integrality
• Tests for netCDF round-trip of relaxed registry
• Test that relaxing all variables converts MILP to LP (m.type)
• All 56 tests in test_fix_relax.py pass

🤖 Generated with Claude Code

[FBumann]

@FabianHofmann sorry for the noisy notebook! The rest should be easy to review.

[FBumann]

I'll need to adjust this before merge.

[FBumann]

@FabianHofmann ready

[FabianHofmann]

• unfix() delegates to unrelax() so the full fix+relax workflow is undone in one call

The code does not show this. can you check if that is intended? it seems independent from each other

[FBumann]

@FabianHofmann Thats was a stale statement from the PR description!
fixing and relaxing are now completely decoupled. A user that wants the fix and relax worflow for getting duals needs to call both methods. Thats clearer and more versatile.

[FabianHofmann]

Feel free to merge