Research

Nonsmooth Convex Optimization using the Specular Gradient Method with Root-Linear Convergence

Geometry and Probability 2024, Fukuoka University, Yamagata, Japan, 2025    |   Talk

• Proved that a specular derivative is a subderivative in the one-dimensional Euclidean space. 

• Defined the specular gradient method to select a specular derivative as a subgradient in the subgradient method in the one-dimensional Euclidean space

• Proved the root-linear convergence rate of the specular gradient method in the one-dimensional Euclidean space.

• Implemented four examples. 

• Provided a Python package on GitHub.

The specular derivative and its application to the wave equation

2023 KMS Spring Meeting, Korean Mathematical Society, 2023    |    Poster Presentation    

Masters' thesis, 2022    |   Talk

• Well-defined specular derivatives and specular spaces in n-dimensional Euclidean spaces.

• Proved the Quasi-Rolles' Theorem and the Quasi-Mean Value Theorem in the specular derivative sense.

• Proved the 2nd order specular differentiability implies the 1st order classical differentiability.

• Proved the 1st form and the 2nd form of the Fundamental Theorem of Calculus in the specular derivative sense.

• Extended the concept of the gradient and the directional derivative in the specular derivative sense.

• Found the condition when specular normal vectors exist.

• Constructed and solved the 1st order ordinary differential equation, the transport equation, and the wave equation with specular derivatives.

Primality between Consecutive Primorials

2022 KMS Spring Meeting, Korean Mathematical Society, 2022    |    Poster Presentation    

2022 YNMS Annual Meeting, Youngnam Mathematical Society, 2022    |    Talk

• Proved the base providing the most efficient primality test is the primorial.

• Established a necessary and sufficient condition for a positive integer in between consecutive primorials to be determined as a prime number.

Valuation of condor spreads through a variational inequality approach

2021 KSIAM Annual Meeting, Korean Society for Industrial and Applied Mathematics, 2021    |    Poster Presentation

• Performed the given PDE with Finite Difference Method by using Python

• Visualized the solution, the obstacle function, and free boundaries

Numerical Simulation for Free boundary of the Option Price Determining Partial Differential Equation Model

Undergraduate Research Internship Program, College of Natural Science, Kyungpook National University, 2021    |    Poster Presentation

• Performed the given PDE with Finite Difference Method by using Python

• Visualized the solution, the obstacle function, and free boundaries

Prime Number Decision Algorithm Studying Shift and Product of Number System

The 26th Contest for Student Academic Research, KMU, 2019    |    Description Paper and PPT Presentation

• Proved the formula converting a positive integer represented decimal system to other number systems with arbitrary base

• Proved the relationship between number systems and prime numbers

• Suggested the algorithm deciding whether any positive integer is prime or not 

• Programmed previous theorems as executable file by using Python 

Machine Learning Model for Detecting Moving Objects

Forum on Career Leaders for Next-Generation Women's Mathematical Sciences, Korean Women in Mathematical Sciences, 2019    |    Poster Presentation

• Suggested algorithm deciding whether detected moving objects are wild boars or not

• Analyzed the patterns of moving objects by using k-means clustering

• Performed supervised learning with 83% accuracy by using Keras