This paper is motivated by the fact that mixed integer nonlinear programming is an important and difficult area for which there is a need for developing new methods and software for solving large-scale problems. Moreover, both fundamental building blocks, namely mixed integer linear programming and nonlinear programming, have seen considerable and steady progress in recent years. Wishing to exploit expertise in these areas as well as on previous work in mixed integer nonlinear programming, this work represents the first step in an ongoing and ambitious project within an open-source environment. COIN-OR is our chosen environment for the development of the optimization software. A class of hybrid algorithms, of which ‘branch and bound’ and ‘polyhedral outer approximation’ are the two extreme cases, is proposed and implemented. Computational results that demonstrate the effectiveness of this framework are reported, and a library of mixed integer nonlinear problems that exhibit convex continuous relaxations is made publicly available.
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