1 research outputs found
A Status Report on Conflict Analysis in Mixed Integer Nonlinear Programming
Mixed integer nonlinear programs (MINLPs) are arguably among the hardest
optimization problems, with a wide range of applications. MINLP solvers that
are based on linear relaxations and spatial branching work similar as mixed
integer programming (MIP) solvers in the sense that they are based on a
branch-and-cut algorithm, enhanced by various heuristics, domain propagation,
and presolving techniques. However, the analysis of infeasible subproblems,
which is an important component of most major MIP solvers, has been hardly
studied in the context of MINLPs. There are two main approaches for
infeasibility analysis in MIP solvers: conflict graph analysis, which
originates from artificial intelligence and constraint programming, and dual
ray analysis.
The main contribution of this short paper is twofold. Firstly, we present the
first computational study regarding the impact of dual ray analysis on convex
and nonconvex MINLPs. In that context, we introduce a modified generation of
infeasibility proofs that incorporates linearization cuts that are only locally
valid. Secondly, we describe an extension of conflict analysis that works
directly with the nonlinear relaxation of convex MINLPs instead of considering
a linear relaxation. This is work-in-progress, and this short paper is meant to
present first theoretical considerations without a computational study for that
part