arXiv subjects

Daniel de Roux

Publications and source records attributed to Daniel de Roux.

3 recordsLinked to original sources

arXiv2025

Hybrid Quantum Branch-and-Bound Method for Quadratic Unconstrained Binary Optimization

Quantum algorithms have shown promise in solving Quadratic Unconstrained Binary Optimization (QUBO) problems, benefiting from their connection to the transverse field Ising model. Various Ising solvers, both classical and quantum, have emerged to tackle such problems efficiently but lack global optimality guarantees and often suffer from hardware limitations such as limited qubit availability. In this work, we propose a hybrid branch-and-bound (B&B) framework that integrates Ising solvers as heuristics within a classical B&B algorithm. Unlike prior theoretical studies, our work presents a practical implementation, available as open-source on GitHub. We explore when and where to apply Ising solvers in the search tree and introduce a custom branching rule optimized QUBO embedding. Our method is evaluated on hundreds of QUBO instances from QUBOLib.jl using Gurobi and the D-Wave quantum annealer. Our results show up to 11% less solution time and 17% fewer nodes compared to default Gurobi, an off-the-shelf commercial optimization solver. These findings demonstrate the value of hybrid quantum-classical strategies for enhancing exact optimization.

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arXiv2025

Spectral Outer-Approximation Algorithms for Binary Semidefinite Problems

Integer semidefinite programming (ISDP) has recently gained attention due to its connection to binary quadratically constrained quadratic programs (BQCQPs), which can be exactly reformulated as binary semidefinite programs (BSDPs). However, it remains unclear whether this reformulation effectively uses existing ISDP solvers to address BQCQPs. To the best of our knowledge, no specialized ISDP algorithms exploit the unique structure of BSDPs derived from BQCQPs. This paper proposes a novel spectral outer approximation algorithm tailored for BSDPs derived from BQCQP reformulations. Our approach is inspired by polyhedral and second-order representable regions that outer approximate the feasible set of a semidefinite program relying on a spectral decomposition of a matrix that simultaneously diagonalizes the objective matrix and an aggregation of the constraint matrices. Computational experiments show that our algorithm is competitive with, and in some cases outperforms, state-of-the-art ISDP solvers such as SCIP-SDP and PAJARITO, highlighting ISDP's potential for solving BQCQPs.

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arXiv2023

Instance-specific linear relaxations of semidefinite optimization problems

We introduce a generic technique to obtain linear relaxations of semidefinite programs with provable guarantees based on the commutativity of the constraint and the objective matrices. We study conditions under which the optimal value of the SDP and the proposed linear relaxation match, which we then relax to provide a flexible methodology to derive effective linear relaxations. We specialize these results to provide linear programs that approximate well-known semidefinite programs for the max cut problem proposed by Poljak and Rendl, and the Lovasz theta number; we prove that the linear program proposed for max cut certifies a known eigenvalue bound for the maximum cut value and is in fact stronger. Our ideas can be used to warm-start algorithms that solve semidefinite programs by iterative polyhedral approximation of the feasible region. We verify this capability through multiple experiments on the max cut semidefinite program, the Lovasz theta number and on three families of semidefinite programs obtained as convex relaxations of certain quadratically constrained quadratic problems.

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