We study split cuts and extended formulations for Mixed Integer Conic Quadratic Programming (MICQP) and their relation to Conic Mixed Integer Rounding (CMIR) cuts. We show that CMIR is a linear split cut for the polyhedral portion of an extended formulation of a quadratic set and it can be weaker than the nonlinear split cut of the same quadratic set. However, we also show that families of CMIR...

Branch-and-Bound (B&B) is perhaps the most fundamental algorithm for the global solution of convex Mixed-Integer Nonlinear Programming (MINLP) problems. It is well-known that carrying out branching in a non-simplistic manner can greatly enhance the practicality of B&B in the context of Mixed-Integer Linear Programming (MILP). No detailed study of branching has heretofore been carried out for MI...

The technical equipment developed and used in both installation and operation processes in refineries, oil and gas pipelines, and gas booster stations has always been expensive. Hence, managers at different organizational levels are keen to find methods to control and reduce these costs. Generally speaking, the operators in a gas booster station choose the operating devices without considering ...

We survey recent progress in applying disjunctive programming theory for the effective solution of mixed integer nonlinear programming problems. Generation of effective cutting planes is discussed for both the convex and nonconvex cases.

In this study, a flexible optimization approach is introduced to design an optimal biocompatible solvent for an extractive fermentation process with cell-recycling. The optimal process/solvent design problem is formulated as a mixed-integer nonlinear programming model in which performance requirements of the compounds are reflected in the objectives and the constraints. A flexible or fuzzy opti...