The primal-dual hybrid gradient (PDHG) method is widely used for convex–concave saddle-point problems, yet its extrapolated variants are typically asymmetric because only one side is extrapolated. We propose a symmetry-preserving refinement, E-...
We study a parameterized SOR-like (PSOR-like) representation of the parameterized inexact Uzawa (PIU) iteration for generalized saddle point systems. An explicit parameter change establishes equivalence to PIU with an exact first-block solve, and to...
In strong-field ionization, complex-time saddle points are closely related to electron emission times and quantum-orbit interference patterns. However, not all solutions to the saddle-point equation carry physical contributions. Saddle coalescence ca...
Further measurements of delay time, in the transfer of modulation between microwave beams, are reported even considering the angular dependence in the orientation of the
In order to overcome the computational challenges associated with block preconditioners for Krylov subspace methods, particularly those arising from Schur complement systems, this paper proposes an improved new block (INB) preconditioner for solving...
Recently, the adaptive regularized proximal quasi-Newton (ARPQN) method has demonstrated a strong performance in solving composite optimization problems over the Stiefel manifold. However, its reliance on first-order information limits its applicabil...
In this paper, we consider the numerical solution of the optimal control problems of the elliptic partial differential equation. Numerically tackling these problems using the finite element method produces a large block coupled algebraic system of eq...
Recently, many stochastic Alternating Direction Methods of Multipliers (ADMMs) have been proposed to solve large-scale machine learning problems. However, for large-scale saddle-point problems, the state-of-the-art (SOTA) stochastic ADMMs still have...
Advancement in physics often results from analyzing numerical data and then creating a theoretical model that can explain and predict those data. In the field of lens design, the reverse is true: longstanding theoretical understanding is being overta...
In this paper, we propose an incremental-type subgradient scheme for solving a nonsmooth convex–concave minimax optimization problem in the setting of Euclidean spaces. We investigate convergence results by deriving an upper bound for the absol...
In many fields of science and engineering, partial differential equation (PDE) constrained optimal control problems are widely used. We mainly solve the optimization problem constrained by the time-periodic eddy current equation in this paper. We pro...
In this paper we present an appropriate singular, zero-sum, linear-quadratic differential game. One of the main features of this game is that the weight matrix of the minimizer’s control cost in the cost functional is singular. Due to this singularit...
In this paper, we introduce a new class of multi-dimensional robust optimization problems (named
In this paper, we investigate the accuracy and robustness of three classes of methods for solving two-phase incompressible flows on a staggered grid. Here, the unsteady two-phase flow equations are simulated by finite volumes and penalty methods usin...
Experimental results of delay-time measurements in the transfer of modulation between microwave beams, as reported in previous articles, were interpreted on a competition (interference) between two waves, one of which is modulated and the other is a...
Patterns within strings enable us to extract vital information regarding a string’s randomness. Understanding whether a string is random (Showing no to little repetition in patterns) or periodic (showing repetitions in patterns) are described b...
In the present paper, we study the high-order above-threshold ionization of noble-gas atoms using a bi-elliptic orthogonal two-color (BEOTC) field. We give an overview of the SFA theory and calculate the differential ionization rate for various value...
We derive the eigenvalue bounds for symmetric block-tridiagonal multiple saddle-point systems preconditioned with the symmetric positive definite (SPD) preconditioner proposed by J. Pearson and A. Potschka in 2024 and further studied by L. Bergamasch...
Multibody dynamics (MBD) simulations involving hundreds to thousands of bodies give rise to large-scale, sparse, and structurally indefinite linear systems. Traditional direct solvers incur prohibitive memory and computational costs, while iterative...
This paper asks whether group distributionally robust optimisation raises the worst-group macro-F1 of a block-masked multimodal logistic regression with availability indicators for multilingual fact-checking. Stochastic Mirror-Prox solves the resulti...
Given the mutual information of finite-alphabet inputs cannot be calculated concisely and accurately over fading channels, this paper proposes a new method to calculate the mutual information. First, the applicability of the saddle point method is st...
To determine the photon emission or absorption probability for a diatomic system in the context of the semiclassical approximation it is necessary to calculate the characteristic canonical oscillatory integral which has one or more saddle points. Int...
In order to accurately simulate the position of the saddle in the analysis and calculation of a suspension bridge, and then obtain the accurate shape of the datum strand in the construction site, this paper puts forward a calculation method on the po...
Thermography is a non-invasive method for measuring surface temperatures and may be a convenient way of identifying hypo/hyperthermic areas under a saddle that may be related to saddle pressures. A thermal camera quantified minimum/maximum/mean tempe...
This mathematical model explains the behavior of sinusoidal radius activity in stagnation point three-dimensional flow of hybrid nanoparticles through a circular cylinder. The energy equation of heat source/sink effect and the mass equation of Arrhen...
Terrain feature points, such as the peaks and saddles, are the basic framework of surface topography and its undulations, which significantly affect the spatial distribution of surface topography. In the past, terrain feature points were extracted se...
We construct global phase portraits of inflationary dynamics in teleparallel gravity models with a scalar field nonminimally coupled to torsion scalar. The adopted set of variables can clearly distinguish between different asymptotic states as fixed...
Weighted problems for the p-Laplacian represent a wide range of models arising from real-world research. Solving such problems involves, in many situations, variational approaches that are various and a virtually inexhaustible resource. In this paper...
The effect of external and internal elastic strain fields on the anisotropic diffusion of radiation defects (RDs) can be taken into account if one knows the dipole tensor of saddle-point configurations of the diffusing RDs. It is usually calculated b...
In this paper, a method for extracting Fenglin and Fengcong landform units based on karst topographic feature points is proposed. First, the variable analysis window method is used to extract peaks, nadirs, and saddle points in the karst area based o...
A karst depression is an important sign of the development stage of karst landforms. The morphological characteristics of depressions can help reflect the development and evolution process of such landforms. The accurate identification and extraction...
The uncertainty in the new power system has increased, leading to limitations in traditional stability analysis methods. Therefore, considering the perspective of the three-dimensional static security region (SSR), we propose a novel approach for sys...
Given the relevance and wide use of the Generative Adversarial (GA) methodology, this paper focuses on finite samples to better understand its benefits and pitfalls. We focus on its finite-sample properties from both statistical and numerical perspec...
In this work, we consider the monotone inclusion problem in real Hilbert spaces and propose a simple inertial method that does not include any evaluations of the associated resolvent and projection. Under suitable assumptions, we establish the strong...
This article proposes asymptotic methods for calculating Sommerfeld integrals, which enable us to calculate the integral using the expansion of a function into an infinite power series at the saddle point, where the role of a rapidly oscillating func...
To reduce mold costs in composite forming, multi-point tooling technology has been integrated into the hot diaphragm forming process. However, this approach still faces several challenges, including time-consuming prepreg layup, high energy consumpti...
We propose a new alternating direction method of multipliers (ADMM) with an optimal parameter for the unilateral obstacle problem. We first use the five-point difference scheme to discretize the problem. Then, we present an augmented Lagrangian by in...
In the framework of the Polyakov quark-meson model with two flavors, the bubble dynamics of a first-order phase transition in the region of high density and low temperature are investigated by using the homogeneous thermal nucleation theory. In mean-...
In this paper, we introduce a triple Mann iteration method for approximating an element in the set of common solutions of a system of quasivariational inclusion issues, which is an equilibrium problem and a common fixed point problem (CFPP) of finite...
Feature-based retinal fundus image registration (RIR) technique aligns fundus images according to geometrical transformations estimated between feature point correspondences. To ensure accurate registration, the feature points extracted must be from...
In this paper, a new three-dimensional fractional-order Hopfield-type neural network with delay is proposed. The system has a unique equilibrium point at the origin, which is a saddle point with index two, hence unstable. Intermittent chaos is found...
A plethora of applications in non-linear analysis, including minimax problems, mathematical programming, the fixed-point problems, saddle-point problems, penalization and complementary problems, may be framed as a problem of equilibrium. Most of the...
We consider field theory formulation for directed polymers and interfaces in the presence of quenched disorder. We write a series representation for the averaged free energy, where all the integer moments of the partition function of the model contri...
This paper investigates the local dynamics of a discrete predator–prey system incorporating an Allee effect and a Holling-IV functional response. After nondimensionalization, a positivity-preserving discrete model is obtained by the semi-discre...
In this paper, we introduce two novel extragradient-like methods to solve variational inequalities in a real Hilbert space. The variational inequality problem is a general mathematical problem in the sense that it unifies several mathematical models,...
The existence of homoclinic orbits or heteroclinic cycle plays a crucial role in chaos research. This paper investigates the existence of the homoclinic orbits to a saddle-focus equilibrium point in several classes of three-dimensional piecewise affi...
In this paper, the uniform approximations of the Apostol–Frobenius–Genocchi polynomials of order α in terms of the hyperbolic functions are derived through the saddle-point method. Moreover, motivated by the works of Corcino et al.,...
We have theoretically investigated nine unusual isomers of the molecular formula C5H4 using coupled cluster (CC) and density functional theory (DFT) methods. These molecules possess non-classical structures consisting of two pyramidanes, three planar...
Time-dependent reliability analysis (TRA) is essential for the life-cycle risk assessment of engineering systems. However, existing TRA methods often require extensive statistical data or computationally expensive surrogate models, which limit their...
In the paper, nonlinear vibration characteristics of a rotor system are investigated. Such a nonlinear rotor system is subjected to brush seal forces, which are obtained by integrating the bristle force along the entire ring. The nonlinear brush seal...
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