Mixed-integer quadratically constrained quadratic program- ming (MIQCQP) is a general class related to several impor- tant problems such as polynomial, semidefinite, and conic programming. Moreover, MIQCQP is a natural way to model many important problems in chemical engineering applica- tions. Our motivation is the refinery operational planning problem (ROPP) under uncertainty, which has a large-scale deterministic equivalent MIQCQP. We tackle this problem proposing a primal-dual decomposition algorithm named the p-Lagrangian method, which combines a bundle-method inspired Lagrangian decomposition with MIP-based relax- ations. These relaxations are obtained using the normalised multiparametric desegregation technique (NMDT) and can be made arbitrarily precise by means of a precision parameter p. We present enhancements for the NMDT-based relaxation and how to effectively employ them in the decomposition algorithm. The proposed method was tested on a real-world ROPP and compared with the commercial solver BARON in terms of performance. The numerical results obtained illus- trate the efficiency of the method for several instances.
International Symposium on Mathematical Programming