Solving mixed-integer nonlinear optimization problems using simultaneous convexification: a case study for gas networks

Abstract Solving mixed-integer nonlinear optimization problems (MINLPs) to global optimality is extremely challenging. An important step for enabling their solution consists in the design of convex relaxations feasible set. Known approaches based on spatial branch-and-bound become more effective tighter used are. Relaxations are commonly established by underestimators, where each constraint function considered separately. Instead, a considerably relaxation can be found via so-called simultaneous convexification, underestimators derived than one at time. In this work, we present approach solving that uses convexification. We introduce separation method relies determining envelope linear combinations functions and nonsmooth problem. particular, apply quadratic absolute value derive envelopes. The practicality proposed demonstrated several test instances from gas network optimization, outperforms standard use separate relaxations.