Applications and algorithms for mixed integer nonlinear programming

Applications and algorithms for mixed integer nonlinear programming

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...

Mixed Integer Nonlinear Programming Applications

In this contribution we apply different approaches to solve four rather different MINLP problems: special extensions to time-indexed formulations of production planning problems, a production planning problem in BASF’s petrochemical division, a site analysis of one of BASF’s bigger sites, and a process design problem. The first problem is related to a useful nonlinear extension of production pl...

Mixed-Integer Nonlinear Programming

Recently, the area of Mixed Integer Nonlinear Programming (MINLP) has experienced tremendous growth and a flourish of research activity. In this article we will give a brief overview of past developments in the MINLP arena and discuss some of the future work that can foster the development of MINLP in general and, in particular, robust solver technology for the practical solution of problems.

Deterministic Methods for Mixed Integer Nonlinear Programming

Algorithms for Stochastic Mixed-Integer Programming Models

In this chapter, we will study algorithms for both two-stage as well as multi-stage stochastic mixed-integer programs. We present stagewise (resourcedirective) decomposition methods for two-stage models, and scenario (pricedirective) decomposition methods for multi-stage models. The manner in which these models are decomposed relies not only on the specific data elements that are random, but al...