Year: 2017
Type: preprint
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 via 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.
Source: arXiv (Cornell University)
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: China Medical University
Awards: G2550844701, G5797768028
OpenAlex ID: W2950880637