Proximal Point Research Articles

Inertial proximal point algorithm for the split common solution problem of monotone operator equations

Inertial proximal point algorithm for the split common solution problem of monotone operator equations

How a Subclinical Unilateral Vestibular Signal Improves Binocular Vision.

The present study aimed to determine if an infra-liminal asymmetric vestibular signal could account for some of the visual complaints commonly encountered in chronic vestibular patients. We used infra-liminal galvanic vestibular stimulation (GVS) to investigate its potential effects on visuo-oculomotor behavior. A total of 78 healthy volunteers, 34 aged from 20 to 25 years old and 44 aged from 40 to 60 years old, were included in a crossover study to assess the impact of infra-liminal stimulation on convergence, divergence, proximal convergence point, and stereopsis. Under GVS stimulation, a repeated measures ANOVA showed a significant variation in near convergence (p < 0.001), far convergence (p < 0.001), and far divergence (p = 0.052). We also observed an unexpected effect of instantaneous blocking of the retest effect on the far divergence measurement. Further investigations are necessary to establish causal relationships, but GVS could be considered a behavioral modulator in non-pharmacological vestibular therapies.

Referencing the center of the femoral head during robotic or computer-navigated primary total knee arthroplasty results in less femoral component flexion than the traditional intramedullary axis

BackgroundDuring robotic and computer-navigated primary total knee arthroplasty (TKA), the center of the femoral head is utilized as the proximal reference point for femoral component position rather than the intramedullary axis. We sought to analyze the effect on femoral component flexion–extension position between these two reference points. MethodsWe obtained CT 3D-reconstructions of 50 cadaveric intact femurs. We defined the navigation axis as the line from center of the femoral head to center of the knee (lowest point of the trochlear groove) and the intramedullary axis as the line from center of the knee to center of the canal at the isthmus. Differences between these axes in the sagittal plane were measured. Degree of femoral bow and femoral neck anteversion were correlated with the differences between the two femoral axes. ResultsOn average, the navigated axis was 1.4° (range, −1.4° to 4.1°) posterior to the intramedullary axis. As such, the femoral component would have on average 1.4° less flexion compared with techniques referencing the intramedullary canal. A more anterior intramedullary compared with navigated axis (i.e., less femoral flexion) was associated with more femoral bow (R2 = 0.7, P < 0.001) and less femoral neck anteversion (R2 = 0.5, P < 0.05). ConclusionComputer-navigated or robotic TKA in which the center of the femoral head is utilized as a reference point, results in 1.4° less femoral component flexion than would be achieved by referencing the intramedullary canal. Surgeons should be aware of these differences as they may ultimately influence knee kinematics.

On best proximity point theorems for relatively nonexpansive mappings in locally convex spaces

Abstract This paper explores the concept of normal structure by introducing a generalized form known as P-proximal normal structure. Focusing on the framework of Hausdorff locally convex spaces, the study establishes optimal proximity outcomes for both cyclic and noncyclic relatively P-nonexpansive mappings. Furthermore, the paper presents in the realm of probabilistic normed spaces, considered as instances of Hausdorff locally convex spaces, some theorems that address the existence of best proximity points within this context.

Syndetic proximal set in topological transformation group

In this paper will study the syndetic set in topological transformation group. It represents one of the most important sets in topological dynamics that Gottschak referred .We Introduce dynamical relationship between syndetic set and translation (left-right) ,In topological dynamics group present semi replet set and extensive set .We referred to the relationship of semi replet set and extensive set on the one hand, and their relationship to syndetic set on the other hand . We introduced a new concept syndetic proximal point that depended on syndetic set we indicated a relationship syndetic proximal point with proximal point and extensive proximal point , conclude a number of relationships and concepts

Proximal point method with Bregman distance for quasiconvex pseudomonotone equilibrium problems

In this paper, we propose a proximal point method by using Bregman distance to solve the quasiconvex pseudomonotone equilibrium problems. Under suitable assumptions, we prove that the proposed algorithm is well defined and the sequence generated by it converges to a solution of the equilibrium problem, whenever the bifunction is strongly quasiconvex in its second argument. Our method goes beyond the usual assumption of the bifunction's convexity in the second argument, extending the validity of the convergence analysis of proximal point methods for equilibrium problems. For a particular choice of the Bregman function, our method reduces to the traditional proximal point method. At the end, we illustrate our algorithm and convergence result by numerical examples.

Sulfuric acid pretreatment of oxidized pyrrhotite in flotation desulphurization of magnetite concentrate

The impact of sulfuric acid pretreatment on the surface property of oxidized pyrrhotite (OX-pyrrhotite) and its application in flotation desulphurization of magnetite concentrate were investigated in this study. OX-pyrrhotite using sodium butyl xanthate (BX) collector performed a poor floatability. After sulfuric acid pretreatment, OX-pyrrhotite exposed a new sulphide surface similar to raw pyrrhotite. XPS analysis indicated that the oxidized species such as sulphate were dissolved away from the OX-pyrrhotite surface. This conversion made the natural hydrophobicity and isoelectric point of OX-pyrrhotite proximity to pyrrhotite. Contact angle and zeta potential measurements showed that the sulfuric acid pretreatment increased the adsorption of BX collector and the hydrophobicity of OX-pyrrhotite surface. FTIR and XPS analyses inferred that there existed weak adsorption of BX collector on OX-pyrrhotite surfaces. After sulfuric acid pretreatment, the interaction between BX collector and OX-pyrrhotite surfaces was strengthened, generating dixanthogen species. Therefore, the sulfuric acid pretreatment improved the floatability of OX-pyrrhotite within a wide pH region. When sulfuric acid pretreatment was adopted, the flotation desulfurization could decrease the sulfur content of magnetite concentrate from 4.50% to 0.18%.

A generalized proximal point algorithm with new step size update for solving monotone variational inequalities in real Hilbert spaces

The aim of this paper is to study a generalized version of proximal method with a new step size update for solving variational inequality problem in Hilbert spaces. Weak convergence of the proposed scheme is attained under some appropriate assumptions imposed on the operators and parameters. At the same time, we set up an R-linear convergence rate of our method when the operator is strong monotone. Numerical experiments are given to demonstrate the efficacy of our proposed iterative algorithm. Several versions of recently proposed methods in the literature are special cases of our method.

The Best Proximity Point Problem for New Types of Ciric a 􀀀b􀀀 Contraction with Application

The Best Proximity Point Problem for New Types of Ciric a 􀀀b􀀀 Contraction with Application

C-RSA: Byzantine-robust and communication-efficient distributed learning in the non-convex and non-IID regime

The emerging federated learning applications raise challenges of Byzantine-robustness and communication efficiency in distributed non-convex learning over non-IID data. To address these issues, in this paper we propose a compressed Byzantine-robust stochastic model aggregation method, abbreviated as C-RSA. C-RSA utilizes robust stochastic model aggregation to obtain Byzantine-robustness over non-IID data, and compresses the transmitted messages for achieving high communication efficiency. Theoretically, we exploit Moreau envelope and proximal point projection as technical tools to analyze the convergence of C-RSA for distributed non-convex learning. Extensive numerical experiments are conducted on neural network training tasks to demonstrate the superior performance of C-RSA.

Geraghty–Pata–Suzuki-Type Proximal Contractions and Related Coincidence Best Proximity Point Results

The objective of this research paper is to establish the existence and uniqueness of the best proximity and coincidence with best proximity point results, specifically focusing on Geraghty–Pata–Suzuki-type proximal mappings. To achieve this, we introduce three types of mappings, all within the context of a complete metric space: an α-θ-Geraghty–Pata–Suzuki-type proximal contraction; an α-θ-generalized Geraghty–Pata–Suzuki-type proximal contraction; and an α-θ-modified Geraghty–Pata–Suzuki-type proximal contraction. These new results generalize, extend, and unify various results from the existing literature. Symmetry plays a crucial role in solving nonlinear problems in operator theory, and the variables involved in the metric space are symmetric. Several illustrative examples are provided to showcase the superiority of our results over existing approaches.

Global optimum solutions for a system of (k, ψ)-Hilfer fractional differential equations: Best proximity point approach

Abstract In this article, a class of cyclic (noncyclic) operators are defined on Banach spaces via concept of measure of noncompactness using some abstract functions. The best proximity point (pair) results are manifested for the said operators. The obtained main results are applied to demonstrate the existence of optimum solutions of a system of fractional differential equations involving ( k , ψ ) \left(k,\psi ) -Hilfer fractional derivatives.

Existence of Best Proximity Point in O-CompleteMetric Spaces

In this work, we prove the existence of the best proximity point results for ⊥-contraction (orthogonal-contraction) mappings on an O-complete metric space (orthogonal-complete metric space). Subsequently, these existence results are employed to establish the common best proximity point result. Finally, we provide suitable examples to demonstrate the validity of our results.

On the Linear Convergence of Extragradient Methods for Nonconvex–Nonconcave Minimax Problems

Recently, minimax optimization has received renewed focus due to modern applications in machine learning, robust optimization, and reinforcement learning. The scale of these applications naturally leads to the use of first-order methods. However, the nonconvexities and nonconcavities present in these problems, prevents the application of typical gradient descent/ascent, which is known to diverge even in bilinear problems. Recently, it was shown that the proximal point method (PPM) converges linearly for a family of nonconvex–nonconcave problems. In this paper, we study the convergence of a damped version of the extragradient method (EGM), which avoids potentially costly proximal computations, relying only on gradient evaluation. We show that the EGM converges linearly for smooth minimax optimization problems satisfying the same nonconvex–nonconcave condition needed by the PPM. Funding: H. Lu was supported by The University of Chicago Booth School of Business Benjamin Grimmer was supported by Johns Hopkins Applied Mathematics and Statistics Department.

Numerical Simulation on Crack–Inclusion Interaction for Rib-to-Deck Welded Joints in Orthotropic Steel Deck

Weld defects such as porosity, inclusion, burn-through, and lack of penetration are difficult to detect and control effectively in an orthotropic steel deck (OSD), which will be a fatigue crack initiation site and lead to several fatigue cracking. The crack growth behavior in defective welded joints is different from that of defect-free joints. This study investigates crack–inclusion interaction for rib-to-deck welded joints in OSDs based on numerical simulation and linear elastic fracture mechanics (LEFM). A refined finite element model of a half U-rib with cracks and inclusions was established by using the FRANC3D-ABAQUS interactive technology. The full processes of the crack–inclusion interaction from approaching and penetrating were accurately simulated. Critical parameters, including the stress intensity factor (SIF), the shape factor, the growth rate, and the growth direction were analyzed. The stiff and soft inclusions amplify and shield the SIF of cracks when the crack grows to the local area of inclusions. During the entire process of crack growth, the soft and stiff inclusion accelerate and inhibit the crack growth, respectively. The stiff inclusion will lead to asymmetric growth of the crack shape, where the portion of the crack away from the inclusions has a higher growth rate. The soft and stiff inclusions will attract and repel the direction of crack growth at the proximal point, respectively.

Convergence Rate of Inexact Proximal Point Algorithms for Operator with Hölder Metric Subregularity

Convergence Rate of Inexact Proximal Point Algorithms for Operator with Hölder Metric Subregularity

Balanced resuscitation and earlier mortality end points: bayesian post hoc analysis of the PROPPR trial

IntroductionThe Pragmatic Randomized Optimal Platelet and Plasma Ratios (PROPPR) trial failed to demonstrate a mortality difference for hemorrhaging patients receiving a balanced (1:1:1) vs a 1:1:2 resuscitation at 24 hours...

Some Results for Ćirić–Prešić Type Contractions in F-Metric Spaces

In this study, first, we introduce Ćirić–Prešić type contraction in F-metric spaces and prove a fixed point theorem for self mappings. We apply the fixed point results for a second-order differential equation. Therefore, we define Prešić type almost contraction and F-contraction, and we prove some fixed point theorems. In the last section, we prove the best proximity point theorems for Ćirić–Prešić type proximal contraction in F-metric spaces. Our results generalize the existing results in the literature.

Viscosity approximation method for split best proximity point and monotone variational inclusion problem

ABSTRACT To address the split best proximity point and monotone variational inclusion problems in real Hilbert spaces, we present and investigate projection and viscosity approximation methods. Under a few reasonable assumptions, we prove some weak and strong convergence theorems for the aforementioned methods. The efficiency of the proposed method is demonstrated by some numerical examples. Some well-known recent results in this area have been improved, generalized, and extended as an outcome of this paper.

Generalized Common Best Proximity Point Results in Fuzzy Metric Spaces with Application

The symmetry of fuzzy metric spaces has benefits for flexibility, ambiguity tolerance, resilience, compatibility, and applicability. They provide a more comprehensive description of similarity and offer a solid framework for working with ambiguous and imprecise data. We give fuzzy versions of some celebrated iterative mappings. Further, we provide different concrete conditions on the real valued functions J,S:(0,1]→R for the existence of the best proximity point of generalized fuzzy (J,S)-iterative mappings in the setting of fuzzy metric space. Furthermore, we utilize fuzzy versions of J,S-proximal contraction, J,S-interpolative Reich–Rus–Ciric-type proximal contractions, J,S-Kannan type proximal contraction and J,S-interpolative Hardy Roger’s type proximal contraction to examine the common best proximity points in fuzzy metric space. Also, we establish several non-trivial examples and an application to support our results.