Related papers: Method of Successive Projections for Nonnegative I…

Nonlinear parametric inverse problems appear in many applications and are typically very expensive to solve, especially if they involve many measurements. These problems pose huge computational challenges as evaluating the objective…

Recent efforts on solving inverse problems in imaging via deep neural networks use architectures inspired by a fixed number of iterations of an optimization method. The number of iterations is typically quite small due to difficulties in…

The nonlinear inverse problem of exponential data fitting is separable since the fitting function is a linear combination of parameterized exponential functions, thus allowing to solve for the linear coefficients separately from the…

Inverse optimization, determining parameters of an optimization problem that render a given solution optimal, has received increasing attention in recent years. While significant inverse optimization literature exists for convex…

A new iterative technique is presented for solving of initial value problem for certain classes of multidimensional linear and nonlinear partial differential equations. Proposed iterative scheme does not require any discretization,…

Invariant coordinate selection is an unsupervised multivariate data transformation useful in many contexts such as outlier detection or clustering. It is based on the simultaneous diagonalization of two affine equivariant and positive…

Neural network systems describe complex mappings that can be very difficult to understand. In this paper, we study the inverse problem of determining the input images that get mapped to specific neural network classes. Ultimately, we expect…

Imaging inverse problems aim to recover high-dimensional signals from undersampled, noisy measurements, a fundamentally ill-posed task with infinite solutions in the null-space of the sensing operator. To resolve this ambiguity, prior…

This survey reviews variational and iterative methods for reconstructing non-negative solutions of ill-posed problems in infinite-dimensional spaces. We focus on two classes of methods: variational methods based on entropy-minimization or…

We consider a non-polynomial cubic spline to develop the classes of methods for the numerical solution of singularly perturbed two-point boundary value problems. The proposed methods are second and fourth order accurate and applicable to…

Singular value decomposition (SVD) and matrix inversion are ubiquitous in scientific computing. Both tasks are computationally demanding for large scale matrices. Existing algorithms can approximatively solve these problems with a given…

This paper is concerned with the inverse problem of constructing a symmetric nonnegative matrix from realizable spectrum. We reformulate the inverse problem as an underdetermined nonlinear matrix equation over a Riemannian product manifold.…

Variable order differential equations with non-integrable singularities are considered on spatial networks. Properties of the spectrum are established, and the solution of the inverse spectral problem is obtained.

Based on the matrix expression of general nonlinear numerical analogues presented by the present author, this paper proposes a novel philosophy of nonlinear computation and analysis. The nonlinear problems are considered an ill-posed linear…

In this work, we consider a class of convex optimization problems in a real Hilbert space that can be solved by performing a single projection, i.e., by projecting an infeasible point onto the feasible set. Our results improve those…

We develop the first stochastic incremental method for calculating the Moore-Penrose pseudoinverse of a real matrix. By leveraging three alternative characterizations of pseudoinverse matrices, we design three methods for calculating the…

In this paper, we propose a novel primal-dual inexact gradient projection method for nonlinear optimization problems with convex-set constraint. This method only needs inexact computation of the projections onto the convex set for each…

Solving complex optimization problems in engineering and the physical sciences requires repetitive computation of multi-dimensional function derivatives. Commonly, this requires computationally-demanding numerical differentiation such as…

Consider the problem of finding an optimal value of some objective functional subject to constraints over numerical domain. This type of problem arises frequently in practical engineering tasks. Nowdays almost all general methods for…

In this paper we consider a fully third order nonlinear boundary value problem which is of great interest of many researchers. First we establish the existence, uniqueness of solution. Next, we propose simple iterative methods on both…