Fix false infeasibility for badly scaled QPs in daqp_ldp

[Copilot]

For poorly conditioned Hessians combined with a large f, the LDP transformation produces v = R⁻ᵀf with very large norm. The internal objective ||u||² equals roughly ||v||² at the optimum, which was incorrectly exceeding the hard internal limit 2 * settings->fval_bound (default 2e30) and causing DAQP_EXIT_INFEASIBLE on feasible problems. This affects both the direct daqp_ldp path and the inner solve inside daqp_prox.

Example that previously returned INFEASIBLE:

// min 0.5 * 1e-10 * x^2 + 1e13 * x  s.t.  0 <= x <= 1
// x* = 0 (feasible), but ||v||^2 = (f/sqrt(H))^2 = 1e36 >> 2e30 = old limit
H = 1e-10, f = 1e13, bl = 0, bu = 1

Changes

• src/daqp.c — At the start of daqp_ldp, compute v_norm2 = ||work->v||² and use:

  c_float fval_bound = 2 * work->settings->fval_bound + v_norm2;

  This makes the check equivalent to 0.5*(||u||² − ||v||²) > settings->fval_bound — i.e. the actual QP objective exceeds the user-specified bound — which is the correct condition regardless of problem scaling.

• interfaces/daqp-eigen/tests/08_badly_scaled.cpp — Regression test covering:

  • Non-prox path (H = 1e-10, ||v||² ≈ 1e36)
  • Prox path (H = 1e-20, inner daqp_ldp with ||v||² ≈ 1e32)
  • 2-D mixed-scale sanity check (H = diag(1e8, 1e-8))

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