Local-Minima-Preserving Continuous Relaxation of Ising Problems
The generalized Ising problem captures a broad spectrum of hard combinatorial problems, including MAX-CUT, Number Partitioning (NPP), and Maximum Independent Set. In this work, we consider the notion of one-flip local minima for this problem. We construct a polynomial relaxation and prove the landscape equivalence theorem: there exists a one-to-one correspondence between the local minima of the relaxation and the one-flip minima of the original Ising problem. This guarantee reduces the Ising problem to finding the local minima of a smooth function, allowing us to leverage gradient-based optimizers such as ADAM. We demonstrate that our method is scalable and it achieves strong performance ...
| Authors | Debraj Banerjee, Santanu Mahapatra, Kunal N. Chaudhury |
|---|---|
| Primary category | math.OC |
| Published | 29 June 2026 |
| Last updated at source | 29 June 2026 |
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