Improved quadratic cuts for convex mixed-integer nonlinear programs

This paper presents scaled quadratic cuts based on scaling the second-order Taylor expansion terms for the decomposition methods Outer Approximation (OA) and Partial Surrogate Cuts (PSC) used for solving convex Mixed Integer Nonlinear Programing (MINLP). The scaled quadratic cut is proved to be a stricter and tighter underestimation for the convex nonlinear functions than the classical supporting hyperplanes which results in the improvement of efficiency of the OA and PSC based MINLP solution methods. We integrate the strategies of the scaled quadratic cuts with multi-generation cuts with OA and PSC, and develop six types of MINLP solution methods with scaled quadratic cuts. This improvement transforms the master problem of the decomposition methods in a Mixed Integer Quadratically Constrained Programming (MIQCP) problem. Numerical results of benchmark MINLP problems demonstrate the effectiveness of the proposed MINLP solution methods with scaled quadratic cuts. * Corresponding author. E-mail address: [email protected] (Lixin Tang) 2