First- and Second-Order Asymptotic Analysis with Applications in Quasiconvex Optimization
| Autor: | Fabián Flores-Bazán, I. Montenegro, Nicolas Hadjisavvas, Felipe Lara |
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| Rok vydání: | 2016 |
| Předmět: |
Discrete mathematics
Pure mathematics Class (set theory) Asymptotic analysis 021103 operations research Control and Optimization Applied Mathematics 010102 general mathematics 0211 other engineering and technologies Convex set Regular polygon 02 engineering and technology Function (mathematics) Management Science and Operations Research 01 natural sciences Image (mathematics) Mathematics::Group Theory Quasiconvex function Theory of computation 0101 mathematics Mathematics |
| Zdroj: | Journal of Optimization Theory and Applications. 170:372-393 |
| ISSN: | 1573-2878 0022-3239 |
| DOI: | 10.1007/s10957-016-0938-6 |
| Popis: | We use asymptotic analysis to describe in a more systematic way the behavior at the infinity of functions in the convex and quasiconvex case. Starting from the formulae for the first- and second-order asymptotic function in the convex case, we introduce similar notions suitable for dealing with quasiconvex functions. Afterward, by using such notions, a class of quasiconvex vector mappings under which the image of a closed convex set is closed, is introduced; we characterize the nonemptiness and boundedness of the set of minimizers of any lsc quasiconvex function; finally, we also characterize boundedness from below, along lines, of any proper and lsc function. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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