Solving Sparse Mixed-Integer Quadratic Problems: Application to the Unit Commitment Problem with Optimal Power Flow

J. González Díaz, I. Gómez-Casares, P. Belotti, B. Ghaddar

Mixed-Integer Quadratically Constrained Quadratic Programs (MIQCQPs) are central to infrastructure modeling, yet remain notoriously difficult due to the "double hit" of combinatorial complexity and nonconvexity. Traditional methods often struggle to scale, hindering real-world application.

We present a solution framework that tackles sparse MIQCQPs by integrating Semidefinite Programming (SDP) relaxations with chordal decomposition techniques. By exploiting inherent sparsity, our approach decomposes large semidefinite constraints into smaller, more manageable blocks. We demonstrate the efficacy of the proposed framework on the Unit Commitment problem with AC Optimal Power Flow (AC-OPF), a challenging problem coupling discrete switching decisions with nonlinear physics. Results on IEEE test cases (up to 118 buses) show that our framework provides tighter bounds and scales significantly better than state-of-the-art global solvers.

Keywords: optimal power flow, unit commitment, global optimization, mixed-integer nonlinear programming, semidefinite programming

SI Optimización y Aprendizaje Estadístico en Energía
September 3, 2026  9:00 AM
Aula 28

M. Fischetti

Á. M. González Rueda

S. Pineda, J. M. Morales González

I. Repiso López, S. Pineda Morente, J. M. Morales González