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We consider a class of nonsmooth fractional programming problems with fixed-point constraints, where the numerator is convex and the denominator is concave. To solve this problem, we propose splitting algorithms that compute subgradient…

Optimization and Control · Mathematics 2025-09-03 Mootta Prangprakhon , Nimit Nimana

We present the Deep Picard Iteration (DPI) method, a new deep learning approach for solving high-dimensional partial differential equations (PDEs). The core innovation of DPI lies in its use of Picard iteration to reformulate the typically…

Numerical Analysis · Mathematics 2025-07-08 Jiequn Han , Wei Hu , Jihao Long , Yue Zhao

The systems of nonlinear Volterra integral equations of the first kind with jump discontinuous kernels are studied. The iterative numerical method for such nonlinear systems is proposed. Proposed method employs the modified…

Numerical Analysis · Mathematics 2019-10-22 A. N. Tynda , D. N. Sidorov , N. A. Sidorov

We propose a novel numerical method for solving a quadratic vector equation arising in Markovian Binary Trees. The numerical method consists in a fixed point iteration, expressed by means of the Perron vectors of a sequence of nonnegative…

Numerical Analysis · Mathematics 2011-11-08 Beatrice Meini , Federico Poloni

This paper proposes a non-centered parameterization based infinite-dimensional mean-field variational inference (NCP-iMFVI) approach for solving the hierarchical Bayesian inverse problems. This method can generate available estimates from…

Numerical Analysis · Mathematics 2026-02-09 Jiaming Sui , Junxiong Jia

In this work, we will study a numerical method that allows finding an approximation of the exact solution for a in-situ combustion model using the nonlinear mixed complementary method, which is a variation of the Newtons method for solving…

In this paper, we introduce a new problem called the split feasibility and fixed point equality problems (SFFPEP) and propose a new iterative algorithm for solving the problem (SFFPEP) for the class of quasi-nonexpansive mappings in Hilbert…

Functional Analysis · Mathematics 2016-10-10 L. B. Mohammed , A. Kılıçman

Our work presents a new iterative scheme to approximate the fixed points of nonexpansive mapping. The proposed algorithm is constructed to enhance convergence efficiency while preserving theoretical robustness. Under appropriate assumptions…

Functional Analysis · Mathematics 2026-01-12 Nida Izhar Mallick , Izhar Uddin

We study a numerical approximation for a nonlinear variable-order fractional differential equation via an integral equation method. Due to the lack of the monotonicity of the discretization coefficients of the variable-order fractional…

Numerical Analysis · Mathematics 2021-10-12 Xiangcheng Zheng

This article proposes new strategies for solving two-point Fractional order Nonlinear Boundary Value Problems(FN-BVPs) with Robin Boundary Conditions(RBCs). In the new numerical schemes, a two-point FNBVP is transformed into a system of…

Numerical Analysis · Mathematics 2020-10-06 Junseo Lee , Bongsoo Jang , Hyunju Kim

This article introduces an iterative method for solving nonsingular non-Hermitian positive semidefinite systems of linear equations. To construct the iteration process, the coefficient matrix is split into two non-Hermitian positive…

Numerical Analysis · Mathematics 2025-03-05 Davod Khojasteh Salkuyeh , Mohsen Masoudi

This paper is concerned with the variational inequality problem (VIP) over the fixed point set of a quasi-nonexpansive operator. We propose, in particular, an algorithm which entails, at each step, projecting onto a suitably chosen…

Optimization and Control · Mathematics 2013-04-03 Andrzej Cegielski , Aviv Gibali , Simeon Reich , Rafał Zalas

In this paper, we focus on a class of robust vector polynomial optimization problems (RVPOP in short) without any convex assumptions. By combining/improving the utopia point method (a nonlinear scalarization) for vector optimization and…

Optimization and Control · Mathematics 2023-09-25 Tianyi Han , Liguo Jiao , Jae Hyoung Lee , Junping Yin

We have devised a variational sinc collocation method (VSCM) which can be used to obtain accurate numerical solutions to many strong-coupling problems. Sinc functions with an optimal grid spacing are used to solve the linear and non-linear…

Other Condensed Matter · Physics 2009-11-11 Paolo Amore

We propose a conceptually new method for solving nonlinear inverse scattering problems (ISPs) such as are commonly encountered in tomographic ultrasound imaging, seismology and other applications. The method is inspired by the theory of…

Mathematical Physics · Physics 2016-11-02 Howard W. Levinson , Vadim A. Markel

In this paper we consider some non-stationary relaxed synchronous and asynchronous multi-splitting methods for solving the linear complementarity problems with their coefficient matrices being H-matrices. The convergence theorems of the…

Numerical Analysis · Mathematics 2018-03-08 Cuiyu Liu , Chenliang Li

This paper deals with the solving of variational inequality problem where the constrained set is given as the intersection of a number of fixed-point sets. To this end, we present an extrapolated sequential constraint method. At each…

Optimization and Control · Mathematics 2020-06-30 Mootta Prangprakhon , Nimit Nimana

We present a new interior-point potential-reduction algorithm for solving monotone linear complementarity problems (LCPs) that have a particular special structure: their matrix $M\in{\mathbb R}^{n\times n}$ can be decomposed as $M=\Phi U +…

Machine Learning · Computer Science 2013-01-01 Geoffrey J. Gordon

The need to compute the intersections between a line and a high-order curve or surface arises in a large number of finite element applications. Such intersection problems are easy to formulate but hard to solve robustly. We introduce a…

Numerical Analysis · Mathematics 2020-11-09 Xiao Xiao , Laurent Buse , Fehmi Cirak

For a linear complementarity problem, we present a relaxaiton accelerated two-sweep matrix splitting iteration method. The convergence analysis illustrates that the proposed method converges to the exact solution of the linear…

Optimization and Control · Mathematics 2020-12-02 Dongkai Li , Li Wang , Yuying Liu