On Some Generalized Polyhedral Convex Constructions |
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Authors: | Nguyen Ngoc Luan Jen-Chih Yao |
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Affiliation: | 1. Department of Mathematics and Informatics, Hanoi National University of Education, Hanoi, Vietnam;2. Center for General Education, China Medical University, Taichung, Taiwan |
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Abstract: | Generalized polyhedral convex sets, generalized polyhedral convex functions on locally convex Hausdorff topological vector spaces, and the related constructions such as sum of sets, sum of functions, directional derivative, infimal convolution, normal cone, conjugate function, subdifferential are studied thoroughly in this paper. Among other things, we show how a generalized polyhedral convex set can be characterized through the finiteness of the number of its faces. In addition, it is proved that the infimal convolution of a generalized polyhedral convex function and a polyhedral convex function is a polyhedral convex function. The obtained results can be applied to scalar optimization problems described by generalized polyhedral convex sets and generalized polyhedral convex functions. |
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Keywords: | Conjugate function face finite representation generalized polyhedral convex function generalized polyhedral convex set infimal convolution separation theorem |
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