An Algorithmic Framework for MINLP with Separable Non-Convexity

Claudia d'Ambrosio (1) , Jon Lee (2) , Andreas Waechter (2)

1 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
2 IBM Watson Research Center

We present an algorithm for Mixed-Integer Nonlinear Programming (MINLP) problems in which the non-convexity in the objective and constraint functions is manifested as the sum of non-convex univariate functions. We employ a lower bounding convex MINLP relaxation obtained by approximating each non-convex function with a piecewise-convex underestimator that is repeatedly refined. The algorithm is implemented at the level of a modeling language. Favorable numerical results are presented.

Domaines: Recherche opérationnelle [math.OC]

Claudia d'Ambrosio, Jon Lee, Andreas Waechter. An Algorithmic Framework for MINLP with Separable Non-Convexity. Mixed Integer Nonlinear Programming, Springer, pp.315-347, 2012, ⟨10.1007/978-1-4614-1927-3_11⟩. ⟨hal-00758046⟩