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Journal of Convex Analysis 17 (2010), No. 1, 013--033
Copyright Heldermann Verlag 2010

On the Study of Quasipolyhedral Convex Functions

Maria Dolores Fajardo
Dept. of Statistics and Operational Research, Faculty of Sciences, University of Alicante, 03080 Alicante, Spain

Different methods are available to solve a constrained optimization problem where the objective function is convex and the constraint set is specified by a linear system of a finite number of linear inequalities. In particular, the problem can be formulated as an optimization problem with a unique constraint involving a polyhedral function. When the linear system has an arbitrary number of linear inequalities, the problem can also be transformed in such way that the constraint set is specified by a unique constraint involving a lower semi-continuous convex function. If this function is quasipolyhedral, it locally behaves like a polyhedral one, and this fact should allow to design an algorithm to resolve the optimization problem. In view of this new approach, this paper is devoted to study characterizations and properties of the class of quasipolyhedral functions, as well as their conjugate function and their subdifferential.

Keywords: Semi-infinite inequality systems, quasipolyhedral convex sets, subdifferential, conjugate function.

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