5 papers
Specular differentiation in one dimension: a quasi-mean value theorem, regularity, and discontinuities
Kiyuob Jung
We develop a theory of specular differentiation on real intervals. The specular derivative is defined by averaging the angles associated with the forward and backward difference qu…
Specular differentiation in normed vector spaces: Quasi-Mean Value and Quasi-Fermat Theorems
Kiyuob Jung
This paper introduces specular differentiation, which generalizes Gâteaux and Fréchet differentiation in normed vector spaces. We investigate its fundamental theoretical properti…
Specular gradient methods for nonsmooth convex optimization in Euclidean spaces: a subgradient selection strategy
Kiyuob Jung
This paper deals with nonsmooth convex optimization problems in Euclidean spaces. We identify special elements of the subdifferential of a convex function, called specular gradient…
Nonsmooth Convex Optimization using the Specular Gradient Method with Root-Linear Convergence
Kiyuob Jung, Jehan Oh
In this paper, we find the special case of the subgradient method minimizing a one-dimensional real-valued function, which we term the specular gradient method, that converges root…
The Specular Derivative
Kiyuob Jung, Jehan Oh
In this paper, we introduce a new generalized derivative, which we term the specular derivative. We establish the Quasi-Rolles' Theorem, the Quasi-Mean Value Theorem, and the Funda…