On the existence of polyhedral convex envelopes

By F. Tardella. 2004

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ANTIGONE: Algorithms for coNTinuous / Integer Global Optimization of Nonlinear Equations (2014, methodology): “x an n Edge-Concave [100,103,132,133] Exponential transformation [90–92,94] Fractional [116,136] Outer approximation [59,93] Absolute value |a · x + b| Equivalent MILP [104] Representation”
GloMIQO: Global mixed-integer quadratic optimizer (2012, background): “…w xxi , j representing nonlinear term x i · x j is constrained according to its convex hull: Equations (12)–(13) are used at every node of the branch-and-bound tree where the bounds on both x i and x j are ﬁnite (i.e., neither unbounded nor within a predeﬁned ε BOX > 0).”
A review of recent advances in global optimization (2009, background): “Tardella (2003) studied the class of functions whose convex envelope on a polyhedron coincides with the convex envelope based on the polyhedron vertices, and proved important conditions for a vertex polyhedral convex envelope.”