Convex Minlp – An Efficient Tool for Design and Optimization Tasks?

Convex mixed-integer nonlinear programming (MINLP) has reached a certain maturity, and this paper is intended to show that there are efficient solvers available for convex MINLP problems. The presence of efficient solvers, in combination with the extended modeling capabilities compared to mixed-integer linear programming, make convex MINLP an attractive framework for dealing with industry-relevant optimization tasks. In the paper, we describe some frequently used modeling techniques within MINLP, and a numerical comparison shows how these techniques affect some commonly available solvers. Some solver features are also described along with a discussion of future possibilities and challenges for convex MINLP solvers.