Concept record · edition 0.1.0
Penalty term
A term added to an objective so that violating a hard constraint costs more than any feasible improvement, converting a constrained problem into an unconstrained one.
Why it matters
It is how real constraints — budgets, capacities, exclusivity — enter a QUBO at all.
What this does not establish
Penalty multipliers widen the energy scale and worsen conditioning; a formally correct encoding can be numerically much harder to solve than the problem it encodes.
Claims using this concept
Sources
primary paper · identifier verified
Ising formulations of many NP problems
Andrew Lucas · 2013
arXiv:1302.5843
Catalogues explicit Ising encodings for NP-hard problems — the step that turns a combinatorial problem into a spin model a tensor network can act on.
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