Binary MILP (HiGHS)

Track: exact-K binary selection. Method ID: highs.

Linearizes each pairwise binary product using an auxiliary variable and McCormick constraints, then solves the exact-K MILP through SciPy’s HiGHS interface.

Dependencies: Install vqe-portfolio[classical] for SciPy.

Key parameters: time_limit limits native solver time; mip_rel_gap sets its relative-gap target.

Guarantees and limits: The formulation is equivalent to the binary quadratic objective and has quadratic model size. Inspect status, incumbent, lower bound, and gap; a time limit does not imply optimality. Model construction is outside the native time limit.

Example

Use the shared inputs.

from vqe_portfolio.baselines import mixed_integer_binary_baseline

result = mixed_integer_binary_baseline(mu, Sigma, lam=4.0, k=2, time_limit=10.0)