I. Nowak: Relaxation and Decomposition Methods for Mixed Integer Nonlinear Programming

Deterministic Methods for Mixed Integer Nonlinear Programming

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.

Fenchel decomposition for stochastic mixed-integer programming

This paper introduces a new cutting plane method for two-stage stochastic mixed-integer programming (SMIP) called Fenchel decomposition (FD). FD uses a class of valid inequalities termed, FD cuts, which are derived based on Fenchel cutting planes from integer programming. First, we derive FD cuts based on both the first and second-stage variables, and devise an FD algorithm for SMIP and establi...

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 using interior-point methods

In this paper, we outline a bilevel approach for solving mixed integer nonlinear programming problems. The approach combines a branch-and-bound algorithm in the outer iterations and an infeasible interior-point method in the inner iterations. We report on the details of the implementation, including the efficient pruning of the branch-and-bound tree via equilibrium constraints, warmstart strate...