AMBIENTUM BIOETHICA BIOLOGIA CHEMIA DIGITALIA DRAMATICA EDUCATIO ARTIS GYMNAST. ENGINEERING EPHEMERIDES EUROPAEA GEOGRAPHIA GEOLOGIA HISTORIA HISTORIA ARTIUM INFORMATICA IURISPRUDENTIA MATHEMATICA MUSICA NEGOTIA OECONOMICA PHILOLOGIA PHILOSOPHIA PHYSICA POLITICA PSYCHOLOGIA-PAEDAGOGIA SOCIOLOGIA THEOLOGIA CATHOLICA THEOLOGIA CATHOLICA LATIN THEOLOGIA GR.-CATH. VARAD THEOLOGIA ORTHODOXA THEOLOGIA REF. TRANSYLVAN
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STUDIA MATHEMATICA - Ediţia nr.1 din 2022 | |||||||
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QUASICONVEX FUNCTIONS: HOW TO SEPARATE, IF YOU MUST!. Autori: JOHANNES BARTHOLOMEUS GERARDUS FRENK, JOAQUIM ANTÓNIO DOS SANTOS GROMICHO, SHUZHONG ZHANG. |
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Rezumat: DOI: 10.24193/subbmath.2022.1.08 Published Online: 2022-03-10 Published Print: 2022-03-31 pp. 105-128 VIEW PDF FULL PDF Since quasiconvex functions have convex lower level sets it is possible to minimize them by means of separating hyperplanes. An example of such a procedure, well-known for convex functions, is the subgradient method. However, to find the normal vector of a separating hyperplane is in general not easy for the quasiconvex case. This paper attempts to gain some insight into the computational aspects of determining such a normal vector and the geometry of lower level sets of quasiconvex functions. In order to do so, the directional differentiability of quasiconvex functions is thoroughly studied. As a consequence of that study, it is shown that an important subset of quasiconvex functions belongs to the class of quasidifferentiable functions. The main emphasis is, however, on computing actual separators. Some important examples are worked out for illustration. Mathematics Subject Classification (2010): 54AXX. Keywords: Quasiconvex minimization, separation, quasidifferentiability. |
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