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 supporti...

Logistics Network Design includes network configuration decisions having long-standing influences on other tactical and operational decisions. Recently, regarding environmental issues and customer awareness and global warming closed-loop supply chain network design is taken into consideration. The proposed network for the integrated forward and reverse logistics is developed by formulating a cy...

‎in this paper‎, ‎some kkt type sufficient global optimality conditions‎ ‎for general mixed integer nonlinear programming problems with‎ ‎equality and inequality constraints (minpp) are established‎. ‎we achieve‎ ‎this by employing a lagrange function for minpp‎. ‎in addition‎, ‎verifiable sufficient global optimality conditions for general mixed‎ ‎integer quadratic programming problems are der...

‎In this paper‎, ‎some KKT type sufficient global optimality conditions‎ ‎for general mixed integer nonlinear programming problems with‎ ‎equality and inequality constraints (MINPP) are established‎. ‎We achieve‎ ‎this by employing a Lagrange function for MINPP‎. ‎In addition‎, ‎verifiable sufficient global optimality conditions for general mixed‎ ‎integer quadratic programming problems are der...

Mixed-integer quadratic programming (MIQP) is the problem of optimizing a quadratic function over points in a polyhedral set where some of the components are restricted to be integral. In this paper, we prove that the decision version of mixed-integer quadratic programming is in NP, thereby showing that it is NP-complete. This is established by showing that if the decision version of mixed-inte...