A penalty framework for globally solving mixed-integer nonlinear programming problems is presented. Both integrality constraints and nonlinear constraints are handled separately by hyperbolic tangent penalty functions. The preliminary numerical experiments show that the proposed penalty approach is effective and the hyperbolic tangent penalties compete with other popular penalties.

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 work, we present a new hybrid algorithm for convex Mixed Integer Nonlinear Programming combining branch-and-bound and outer approximation algorithms in an e ective and e cient way.

Collection of waste is an important logistic activity within any city. In this study, a mathematical model is proposed in order to reduce the cost of waste collection. First a mixed-integer nonlinear programming model is provided including a waste collection routing problem, so that, there is a balance between the distance between trashcans, and the similarity of the trashcans in terms of th...

This study extends a mathematical model that integrates the location, allocation, inventory replenishment and routing decisions simultaneously. To cope with inherent uncertainty of parameters, we implement a continuous-time Markov process and derive the performance measures of the system. Using the obtained results, the problem is formulated as a mixed integer nonlinear programing model (MINLP)...

Christian Kirches develops a fast numerical algorithm of wide applicability that efficiently solves mixed-integer nonlinear optimal control problems. He uses convexification and relaxation techniques to obtain computationally tractable reformulations for which feasibility and optimality certificates...

The mathematical modeling of systems often requires the use of both nonlinear and discrete components. Discrete decision variables model dichotomies, discontinuities, and general logical relationships. Nonlinear functions are required to accurately represent physical properties such as pressure, stress, temperature, and equilibrium. Problems involving both discrete variables and nonlinear const...

Strong branching is an effective branching technique that can significantly reduce the size of the branch-and-bound tree for solving Mixed Integer Nonlinear Programming (MINLP) problems. The focus of this paper is to demonstrate how to effectively use “discarded” information from strong branching to strengthen relaxations of MINLP problems. Valid inequalities such as branching-based linearizati...

A wide range of optimization problems arising from engineering applications can be formulated as Mixed Integer NonLinear Programmming problems (MINLPs). Duran and Grossmann (1986) suggest an outer approximation scheme for solving a class of MINLPs that are linear in the integer variables by a nite sequence of relaxed MILP master programs and NLP subproblems. Their idea is generalized by treatin...

We present a new tree-search algorithm for solving mixed-integer nonlinear programs (MINLPs). Rather than relying on computationally expensive nonlinear solves at every node of the branchand-bound tree, our algorithm solves a quadratic approximation at every node. We show that the resulting algorithm retains global convergence properties for convex MINLPs, and we present numerical results on a ...