Poorly convex functions and their application to an optimization problem
Volume 47 / 2020
Applicationes Mathematicae 47 (2020), 1-27
MSC: 26B25, 46N10, 52A41.
DOI: 10.4064/am2389-10-2019
Published online: 31 January 2020
Abstract
The paper introduces a new class of functions, called poorly convex, defined on convex subsets of $\mathbb {R}^n$. The class is bigger than the class of classical convex functions, and is a subset of the class of quasi-convex ones. The theory of poorly convex functions is developed, and its application to an optimization problem is shown.
