윤상운 교수

We are concerned with optimization methods for the $L^2$-Wasserstein least squares problem of Gaussian measures (alternatively the $n$-coupling problem). Based on its equivalent form on the convex cone of positive definite matrices of fixed size and the strict convexity of the variance function, we are able to present an implementable (accelerated) gradient method for finding the unique minimizer. Its global convergence rate analysis is provided according to the derived upper bound of Lipschitz

An image restoration problem with Poisson noise arises in many applications of medical imaging, astronomy, and microscopy. To overcome ill-posedness, Total Variation (TV) model is commonly used owing to edge preserving property. Since staircase artifacts are observed in restored smooth regions, higher-order TV regularization is introduced. However, sharpness of edges in the image is also attenuated. To compromise benefits of TV and higher-order TV, the weighted sum of the non-convex TV and non-c

This paper proposes stochastic methods to find an approximate solution for the L 2-Wasserstein least squares problem of Gaussian measures. The variable for the problem is in a set of positive definite matrices. The first proposed stochastic method is a type of clas- sical stochastic gradient methods combined with projection and the second one is a type of variance reduced methods with projection. Their global convergence are analyzed by using the framework of proximal stochastic gradient methods. T

For principal component analysis (PCA) to efficiently analyze large scale matrices, it is crucial to find a few singular vectors in cheaper computational cost and under lower memory requirement. To compute those in a fast and robust way, we propose a new stochastic method. Especially, we adopt the stochastic variance reduced gradient (SVRG) method \cite{JZ} to avoid asymptotically slow convergence in stochastic gradient descent methods. For that purpose, we reformulate the PCA problem as a uncon

In this paper, we present a general family of modified BFGS methods for unconstrained optimization. Under a general form of modified BFGS methods with an undetermined weight function, the family is constructed by determining the weight function based on the analysis of the approximation error to the Hessian matrix. This process gives rise to a novel family of modified BFGS methods with one free parameter, which includes several known methods as special cases. Both the global convergence and the