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Consider using the right-preconditioned GMRES (AB-GMRES) for obtaining the minimum-norm solution of inconsistent underdetermined systems of linear equations. Morikuni (Ph.D. thesis, 2013) showed that for some inconsistent and…

This study investigates a powerful model, targeted to subjective assessments, based on pairwise comparisons. It provides a proof that a distance-based inconsistency reduction transforms an inconsistent pairwise comparisons (PC) matrix into…

In this paper, based on the limited memory techniques and subspace minimization conjugate gradient (SMCG) methods, a regularized limited memory subspace minimization conjugate gradient method is proposed, which contains two types of…

We consider variants of a recently-developed Newton-CG algorithm for nonconvex problems \citep{royer2018newton} in which inexact estimates of the gradient and the Hessian information are used for various steps. Under certain conditions on…

Contrastive Divergence (CD) and Persistent Contrastive Divergence (PCD) are popular methods for training the weights of Restricted Boltzmann Machines. However, both methods use an approximate method for sampling from the model distribution.…

The demands of accuracy in measurements and engineering models today, renders the condition number of problems larger. While a corresponding increase in the precision of floating point numbers ensured a stable computing, the uncertainty in…

In this paper, we propose a novel, computationally efficient reduced order method to solve linear parabolic inverse source problems. Our approach provides accurate numerical solutions without relying on specific training data. The forward…

In this chapter, we investigate recently proposed nonlinear conjugate gradient (NCG) methods for shape optimization problems. We briefly introduce the methods as well as the corresponding theoretical background and investigate their…

Given a full column rank matrix $A \in \mathbb{R}^{m\times n}$ ($m\geq n$), we consider a special class of linear systems of the form $A^\top Ax=A^\top b+c$ with $x, c \in \mathbb{R}^{n}$ and $b \in \mathbb{R}^{m}$. The occurrence of $c$ in…

We propose a new inexact column-and-constraint generation (i-C&CG) method to solve two-stage robust optimization problems. The method allows solutions to the master problems to be inexact, which is desirable when solving large-scale and/or…

In this paper, we study Newton-conjugate gradient (Newton-CG) methods for minimizing a nonconvex function $f$ whose Hessian is $(H_f,\nu)$-H\"older continuous with modulus $H_f>0$ and exponent $\nu\in(0,1]$. Recently proposed Newton-CG…

We propose a two-level nested preconditioned iterative scheme for solving sparse linear systems of equations in which the coefficient matrix is symmetric and indefinite with relatively small number of negative eigenvalues. The proposed…

This paper is concerned with the nonnegative inverse eigenvalue problem of finding a nonnegative matrix such that its spectrum is the prescribed self-conjugate set of complex numbers. We first reformulate the nonnegative inverse eigenvalue…

Stochastic gradient descent (SGD) is a promising method for solving large-scale inverse problems, due to its excellent scalability with respect to data size. In this work, we analyze a new data-driven regularized stochastic gradient descent…

Recent studies have demonstrated that gradient matching-based dataset synthesis, or dataset condensation (DC), methods can achieve state-of-the-art performance when applied to data-efficient learning tasks. However, in this study, we prove…

Incorporating prior information into inverse problems, e.g. via maximum-a-posteriori estimation, is an important technique for facilitating robust inverse problem solutions. In this paper, we devise two novel approaches for linear inverse…

In this paper we introduce a unified analysis of a large family of variants of proximal stochastic gradient descent ({\tt SGD}) which so far have required different intuitions, convergence analyses, have different applications, and which…

This paper is devoted to first-order algorithms for smooth convex optimization with inexact gradients. Unlike the majority of the literature on this topic, we consider the setting of relative rather than absolute inexactness. More…

We proposed a method called residual edge-betweenness gradient (REBG) to enhance synchronizability of networks by assignment of link direction while keeping network topology and link weight unchanged. Direction assignment has been shown to…

Guidance techniques are simple yet effective for improving conditional generation in diffusion models. Albeit their empirical success, the practical implementation of guidance diverges significantly from its theoretical motivation. In this…