42 Results Found

In this paper, we investigate the minimum-norm least squares solution to a quaternion tensor system ${\mathcal{A}}_1{*}_N{\mathcal{X}}_1={\mathcal{C}}_1,$${\mathcal{A}}_1{*}_N{\mathcal{X}}_2+{\mathcal{A}}_2{*}_N{\mathcal{X}}_3={\mathcal{C}}_2,$${\mathcal{E}}_1{*}_N{\mathcal{X}}_1{*}_M{\mathcal{F}}_1+{\mathcal{E}}_1{*}_N{\mathcal{X}}_2{*}_M{\mathcal{F}}_2+{\mathcal{E}}_2{*}_N{\mathcal{X}}_3{*}_M{\mathcal{F}}_2=\mathcal{D}$ by using the Moore–Penrose inverses of block tensors. As an application, we discuss the...

In this work, we study a class of variational inequality problems defined over the intersection of sub-level sets of a countable family of convex functions. We propose a new iterative method for approximating the solution within the framework of Hilb...

In this work, we present numerical methods appropriate for parameter estimation in high-dimensional statistical modelling. The solution of these problems is not unique and a crucial question arises regarding the way that a solution can be found. A co...

This paper presents the Mann-type inertial accelerated subgradient extragradient algorithm with non-monotonic step sizes for solving the split equilibrium and fixed point problems relating to pseudomonotone and Lipschitz-type continuous bifunctions a...

For $G\in {\mathbb{R}}^{m\times n}$ and $g\in {\mathbb{R}}^m$, the minimization ${min\parallel G\psi -g\parallel }_2$, with $\psi \in {\mathbb{R}}^n$, is known as the Tykhonov regularization. We transport the Tykhonov regularization to an infinite-dimensional setting, that is $min\parallel T\left(h\right)\&m$...

Two iterative algorithms are suggested for approximating a solution of the split common fixed point problem involved in pseudo-contractive operators without Lipschitz assumption. We prove that the sequence generated by the first algorithm converges w...

Variational inequality problems (VIPs) provide a versatile framework for modeling a wide range of real-world applications, including those in economics, engineering, transportation, and image processing. In this paper, we propose a novel iterative al...

Column generation is a fundamental technique for solving large-scale combinatorial optimization problems such as unit commitment and vehicle routing, yet its performance is often limited by dual oscillation. This study explores the intrinsic cause of...

This paper develops the linear-algebraic foundations of the Convex Least Squares Programming (CLSP) estimator and constructs its modular two-step convex optimization framework, capable of addressing ill-posed and underdetermined problems. After refor...

In this paper, we propose three variants of Mann-type inertial forward–backward iterative methods for approximating the minimum-norm solution of the monotone inclusion problem and the fixed points of nonexpansive mappings. In the first two meth...

Recently, the split inverse problem has received great research attention due to its several applications in diverse fields. In this paper, we study a new class of split inverse problems called the split variational inequality problem with multiple o...

Finite-dimensional closed-system gate synthesis is a geometric optimal-control problem on a compact Lie group, but global solutions require careful treatment of logarithm branches, determinant-one constraints, drift, anisotropic penalties, and amplit...

In this paper, we explore the least-norm solution to the classical matrix equation $AXB=C$ over the dual quaternion algebra, where A, B, and C are given matrices, while X remains the unknown matrix. We begin by transforming the definition of the Froben...

In this study, a Gaussian process model is utilized to study the Fredholm integral equations of the first kind (FIEFKs). Based on the H–$H_k$ formulation, two cases of FIEFKs are under consideration with respect to the right-hand term: discrete da...

Minimum norm problems consist of finding the distance of a closed subset of a normed space to the origin. Usually, the given closed subset is also asked to be convex, thus resulting in a convex minimum norm problem. There are plenty of techniques and...

In the reconstruction of sparse signals in compressed sensing, the reconstruction algorithm is required to reconstruct the sparsest form of signal. In order to minimize the objective function, minimal norm algorithm and greedy pursuit algorithm are m...

We prove the existence and uniqueness of the solution of the problem of the minimum norm function ${\parallel ·\parallel }_{\infty }$ with a given set of initial coefficients of the trigonometric Fourier series $c_j$ , $j=0,1,\dots ,2n$...

A biharmonic boundary value problem with a singularity is one of the mathematical models of processes in fracture mechanics. It is necessary to have estimates of the function norms in the neighborhood of the singularity point to study the existence a...

In this paper, a novel scheme using hybrid l₁/l₂ norm minimization and the orthogonal matching pursuit (OMP) algorithm is proposed to design the sparse finite impulse response (FIR) decision feedback equalizers (DFE) in multiple input multiple output...

This article outlines the results of comparison methods for representing complex data based on a redundant basis using the L0 norm and analyses the method of a modified MFNN (minimum fuel neural network) and the sparse representation method for the c...

Network interdiction problems involving edge deletion on shortest paths have wide applications. However, in many practical scenarios, the complete removal of edges is infeasible. The minimum-cost shortest-path interdiction problem for trees with the...

The Min–Max control strategy is the most widely used control algorithm for gas turbine engines. This strategy uses minimum and maximum mathematical functions to select the winner of different transient engine control loops at any instantaneous...

The solvability conditions, symmetric solutions, and antisymmetric solutions of matrix equations $AX=B$ are important research topics in matrix theory. As a higher-order generalization of matrices, tensors have made the research on solving tensor equat...

Optical aspherical lenses with high surface quality are increasingly demanded in several applications in medicine, synchrotron, vision, etc. To reach the requested surface quality, most advanced manufacturing processes are used in closed chain with h...

Wireless Sensor Networks (WSN) are of great current interest in the proliferation of technologies. Since the location of the sensors is one of the most interesting issues in WSN, the process of node localization is crucial for any WSN-based applicati...

Bilevel optimization is a fundamental framework for hierarchical decision-making, but its solution is challenging due to the implicit and typically set-valued nature of the lower-level optimality condition. In this paper, we study bilevel optimizatio...

Localizing a moving source by Time Difference of Arrival (TDOA) and Frequency Difference of Arrival (FDOA) commonly requires at least $N+1$ sensors in N-dimensional space to obtain more than N pairs of TDOAs and FDOAs, thereby establishing more than $2N$...

The protection against the unintentional islanding of Grid-Tied inverters is an important electrical security issue addressed by the main Standards. This concern is justified in face of the fact that unintentional islanding can lead to abrupt variati...

This study addresses the multi-stage minimum control energy problem for chain-of-integrator systems, where the objective is to minimize the $L^2$-norm of the control input over a fixed terminal time, subject to boundary conditions and a sequence of inte...

The differential microphone array, or differential beamformer, has attracted much attention for its frequency-invariant beampattern, high directivity factor and compact size. In this work, the design of differential beamformers with small inter-eleme...

We consider choice of the regularization parameter in Tikhonov method if the noise level of the data is unknown. One of the best rules for the heuristic parameter choice is the quasi-optimality criterion where the parameter is chosen as the global mi...

In this paper, we study the effect of detuning parameters and driven external classical field parameters on a quantum system consisting of a ♢-configuration four-level atom inside a quantized cavity field. Under some canonical conditional of dr...

This paper investigates the combined effects of the Maximum Material Condition (MMC) modifier and datum feature shift on hole-group positional tolerance evaluation. The formulation follows ASME Y14.5-2018 as the primary normative framework, with ISO...

Distributed array radar achieves high angular resolution and measurement accuracy, which could provide a solution to suppress digital radio frequency memory (DRFM) repeater jamming. However, owing to the large aperture of a distributed radar, the far...

Uplink–downlink (UL–DL) duality is a standard tool in multiuser transmit optimization. With the beamforming directions held fixed, the downlink power minimization problem and its virtual uplink counterpart are feasible for exactly the sam...

A parking space is the beginning and the end of every car journey. Policies aimed at parking spaces are, thus, an effective way of affecting car travel. Policies regarding parking typically mean setting minimum parking requirements to meet the peak d...

The validation of a feasible application for the production of sustainable bricks with local materials in humid and hot climates, which would allow the current housing needs of a constantly growing population with scarce economic resources to be met...

Brain source imaging and time frequency mapping (TFM) are commonly used in magneto/electro encephalography (M/EEG) imaging. However, these methods suffer from important limitations. Source imaging is based on an ill-posed inverse problem leading to i...

Although wavelet neural networks (WNNs) combine the expressive capability of neural models with multiscale localization, there are currently few theoretical guarantees for their training. We investigate the weight decay (${\mathrm{L}}_2$ regularization) optimizati...

Fractured–vuggy carbonate reservoirs are characterized by highly discrete storage structures, and the number, spatial distribution, and volume of cavities strongly affect well-test responses and reservoir development decisions. This study devel...

Model predictive control, without strict constraints on the control model, effectively overcomes problems, such as poor system dynamic quality caused by time delay, can improve control accuracy to a certain extent, and can directly process input and...

This paper describes the optimal path planning of a redundant finishing mechanism developed for joint space-based additive-finishing integrated manufacturing (AFM). The research motivation results from an inevitable one-sided layout of a finishing st...