In this paper we derive the convex envelope of separable functions obtained as a linear combination of strictly convex coercive one-dimensional functions over compact regions defined by linear combinations of the same one-dimensional functions. As a corollary of the main result, we are able to derive the convex envelope of any quadratic function (not necessarily separable) over any ellipsoid, and the convex envelope of some quadratic functions over a convex region defined by two quadratic constraints.
Convex envelopes of separable functions over regions defined by separable functions of the same type / Locatelli, Marco. - In: OPTIMIZATION LETTERS. - ISSN 1862-4472. - 12:8(2018), pp. 1725-1739. [10.1007/s11590-018-1291-5]
Convex envelopes of separable functions over regions defined by separable functions of the same type
Locatelli, Marco
2018-01-01
Abstract
In this paper we derive the convex envelope of separable functions obtained as a linear combination of strictly convex coercive one-dimensional functions over compact regions defined by linear combinations of the same one-dimensional functions. As a corollary of the main result, we are able to derive the convex envelope of any quadratic function (not necessarily separable) over any ellipsoid, and the convex envelope of some quadratic functions over a convex region defined by two quadratic constraints.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.