Strong Convergence of a General Iterative Algorithm for Mixed Equilibrium, Variational Inequality and Common Fixed Points Problems

The aim of this paper, is to introduce and study a general iterative algorithm concerning the new mappings which the sequences generated by our proposed scheme converge strongly to a common element of the set of solutions of a mixed equilibrium problem, the set of common fixed points of a finite family of nonexpansive mappings and the set of solutions of the variational inequality for a relaxed cocoercive mapping in a real Hilbert space. In addition, we obtain some applications by using this result. The results obtained in this paper generalize and refine some known results in the current literature.

Receded near point of convergence as a predictor of mild cognitive impairment in the general geriatric population:results from a population-based study

AIM:To investigate the relationship between near point of convergence(NPC)and mild cognitive impairment(MCI)in the general elderly population.METHODS:The present report is a part of the Tehran Geriatric Eye Study(TGES):a population-based crosssectional study conducted on individuals 60 years of age and above living in Tehran,Iran using the multi-stage stratified random cluster sampling method.Cognitive status was assessed using the Persian version of the Mini-Mental State Examination(MMSE).All study participants underwent complete ocular examination including measurement of uncorrected and best-corrected visual acuity,objective and subjective refraction,cover testing,NPC measurement,and slit-lamp biomicroscopy.RESULTS:The data of 1190 individuals were analyzed for this report.The mean age of the participants analyzed was 66.82±5.42(60-92y)and 728(61.2%)of them were female.Patients with MCI had a significantly more receded NPC compared to subjects with normal cognitive status(10.89±3.58 vs 7.76±2.71 cm,P<0.001).In the multivariable logistic regression model and in the presence of confounding variables,a receded NPC was statistically significantly associated with an increased risk of MCI(odds ratio:1.334,95%confidence interval:1.263 to 1.410,P<0.001).According to receiver operating characteristic(ROC)analysis,a cut point NPC>8.5 cm(area under the curve:0.764,P<0.001)could predict the presence of MCI with a sensitivity and specificity of 70.9%and 69.5%,respectively.CONCLUSION:A receded NPC can be clinically proposed as a predictor of MCI in older adults.It is recommended that elderly with a receded NPC>8.50 cm undergo detailed cognitive screening for a definite diagnosis of MCI.In this case,the necessary interventions can be carried out to slow down MCI progression to dementia.

EXTREME POINTS AND SUPPORT POINTS OF A CLASS OF ANALYTIC FUNCTIONS

Suppose that {bn} and {cn} are two positive sequences. Let F({bn}, {cn}) ={f(z): f(z) is analytic in and . This article obtains the extreme points and support points of F({bn}, {cn}).

COMPLEX RATIONAL TYPE INTERPOLATION AT DISTURBED FEJR POINTS ON A CURVE

The results of accurate order of uniform approximation and simultaneous approximation in the early work "Jackson Type Theorems on Complex Curves" are improved from Fej'er points to disturbed Fej'er points in this article.Furthermore,the stability of convergence of Tn,ε(f,z) with disturbed sample values f(zk*)+εk are also proved in this article.

THE SUPPORT POINTS AND EXTREME POINTS OF THE UNIT BALL OF H'_P~ 1

By the author denotes the areal measure on the unit disk . Let H’p = {f(z): f(z) is analytic in D and . Let B H ’p and. This article researches the support points and extreme points of B(H’p).

Approximation of Common Fixed Points of Pointwise Asymptotic Nonexpansive Maps in a Hadamard Space

We establish weak and strong convergence of Ishikawa type iterates of two pointwise asymptotic nonexpansive maps in a Hadamard space. For weak and strong convergence results, we drop “rate of convergence condition”, namely (Cn(x)-1)< to answer in the affirma-tive to the open question posed by Tan and Xu [1] even in a general setup.

Strong Convergence of an Iterative Method for Generalized Mixed Equilibrium Problems and Fixed Point Problems

In this paper, we introduce a hybrid iterative method for finding a common element of the set of common solutions of generalized mixed equilibrium problems and the set of common fixed points of an finite family of nonexpansive mappings. Furthermore, we show a strong convergence theorem under some mild conditions.

An Iterative Method for Split Variational Inclusion Problem and Split Fixed Point Problem for Averaged Mappings

In this paper, we use resolvent operator technology to construct a viscosity approximate algorithm to approximate a common solution of split variational inclusion problem and split fixed point problem for an averaged mapping in real Hilbert spaces. Further, we prove that the sequences generated by the proposed iterative method converge strongly to a common solution of split variational inclusion problem and split fixed point problem for averaged mappings which is also the unique solution of the variational inequality problem. The results presented here improve and extend the corresponding results in this area.

Convergence analysis of the corrected Uzawa algorithm for symmetric saddle point problems

For the large sparse saddle point problems,Pan and Li recently proposed in [H. K. Pan,W. Li,Math. Numer. Sinica,2009,31(3): 231-242] a corrected Uzawa algorithm based on a nonlinear Uzawa algorithm with two nonlinear approximate inverses,and gave the detailed convergence analysis. In this paper,we focus on the convergence analysis of this corrected Uzawa algorithm,some inaccuracies in [H. K. Pan,W. Li,Math. Numer. Sinica,2009,31(3): 231-242] are pointed out,and a corrected convergence theorem is presented. A special case of this modified Uzawa algorithm is also discussed.

RAF near point rule for near point of convergence-a short review

RAF near point rule (RNPR) is a routinely used instrument in ophthalmology and optometry practice as well as for research purposes to measure the near point of convergence (NPC). The measurement of NPC is an important criterion for diagnosis and management of convergence insufficiency. The RNPR forms an important tool for ophthalmic clinicians however, only a very little is understood about it. This article tries to describe and review the designs, measurement techniques, merits and demerits of the RNPR and establish the need for its modification. It recommends that clinicians and researchers consider these findings while measuring NPC with the RNPR.

A NEWTON-TYPE GLOBALLY CONVERGENT INTERIOR-POINT METHOD TO SOLVE MULTI-OBJECTIVE OPTIMIZATION PROBLEMS

This paper proposes an interior-point technique for detecting the nondominated points of multi-objective optimization problems using the direction-based cone method.Cone method decomposes the multi-objective optimization problems into a set of single-objective optimization problems.For this set of problems,parametric perturbed KKT conditions are derived.Subsequently,an interior point technique is developed to solve the parametric perturbed KKT conditions.A differentiable merit function is also proposed whose stationary point satisfies the KKT conditions.Under some mild assumptions,the proposed algorithm is shown to be globally convergent.Numerical results of unconstrained and constrained multi-objective optimization test problems are presented.Also,three performance metrics(modified generational distance,hypervolume,inverted generational distance)are used on some test problems to investigate the efficiency of the proposed algorithm.We also compare the results of the proposed algorithm with the results of some other existing popular methods.

Positioning performance analysis on combined GPS/BDS precise point positioning

Combining the observation data from five Multi-GNSS Experiment(MGEX)stations with the precise orbit and clock products from Global Positioning System(GPS)and BeiDou Navigation Satellite System(BDS),we studied the model of combined GPS/BDS precise point positioning,and then analyzed the convergence speed and short-time(6 h)positioning accuracy.The calculation results show that in static positioning,the average convergence time of GPS is about 50 min,and its horizontal accuracy is better than 2 cm while the vertical accuracy is better than 4 cm.The convergence speed of combined GPS/BDS is about 40 min,and its positioning accuracy is close to that of GPS.In kinematic positioning,the average convergence time of GPS is about 72 min,and its horizontal accuracy is better than 5 cm while the vertical accuracy is better than 12 cm.The average convergence time of GPS/BDS is about 57 min,and its horizontal accuracy is better than 3 cm while the vertical accuracy is better than 9 cm.Combined GPS/BDS has significantly improved the convergence speed,and its positioning accuracy is slightly than that of GPS.

VISCOSITY APPROXIMATION METHODS FOR THE SPLIT EQUALITY COMMON FIXED POINT PROBLEM OF QUASI-NONEXPANSIVE OPERATORS

Let H_1, H_2, H_3 be real Hilbert spaces, let A : H_1→ H_3, B : H_2→ H_3 be two bounded linear operators. The split equality common fixed point problem(SECFP) in the infinite-dimensional Hilbert spaces introduced by Moudafi(Alternating CQ-algorithm for convex feasibility and split fixed-point problems. Journal of Nonlinear and Convex Analysis)is to find x ∈ F(U), y ∈ F(T) such that Ax = By,(1)where U : H_1→ H_1 and T : H_2→ H_2 are two nonlinear operators with nonempty fixed point sets F(U) = {x ∈ H_1: Ux = x} and F(T) = {x ∈ H_2: Tx = x}. Note that,by taking B = I and H_2= H_3 in(1), we recover the split fixed point problem originally introduced in Censor and Segal. Recently, Moudafi introduced alternating CQ-algorithms and simultaneous iterative algorithms with weak convergence for the SECFP(1) of firmly quasi-nonexpansive operators. In this paper, we introduce two viscosity iterative algorithms for the SECFP(1) governed by the general class of quasi-nonexpansive operators. We prove the strong convergence of algorithms. Our results improve and extend previously discussed related problems and algorithms.

Stochastic Approximation Method for Fixed Point Problems

We study iterative processes of stochastic approximation for finding fixed points of weakly contractive and nonexpansive operators in Hilbert spaces under the condition that operators are given with random errors. We prove mean square convergence and convergence almost sure (a.s.) of iterative approximations and establish both asymptotic and nonasymptotic estimates of the convergence rate in degenerate and non-degenerate cases. Previously the stochastic approximation algorithms were studied mainly for optimization problems.

AN INFEASIBLE-INTERIOR-POINT PREDICTOR-CORRECTOR ALGORITHM FOR THE SECOND-ORDER CONE PROGRAM

A globally convergent infeasible-interior-point predictor-corrector algorithm is presented for the second-order cone programming (SOCP) by using the Alizadeh– Haeberly–Overton (AHO) search direction. This algorithm does not require the feasibility of the initial points and iteration points. Under suitable assumptions, it is shown that the algorithm can find an ε-approximate solution of an SOCP in at most O(n1/2 ln(ε0/ε)) iterations. The iteration-complexity bound of our algorithm is almost the same as the best known bound of feasible interior point algorithms for the SOCP.

Comparison of availability and reliability among different combined-GNSS/RNSS precise point positioning

With emergence of the BeiDou Navigation Satellite System(BDS), the Galileo Satellite Navigation System(Galileo), the Quasi-Zenith Satellite System(QZSS)and the restoration of the Global Navigation Satellite System(GLONASS), the single Global Positioning System(GPS) has been gradually expanded into multiple global and regional navigation satellite systems(multi-GNSS/RNSS). In view of differences in these 5 systems, a consolidated multi-GNSS/RNSS precise point positioning(PPP) observation model is deduced in this contribution. In addition, the performance evaluation of PPP for multi-GNSS/RNSS is conducted using a large number of the multi-GNSS experiment(MGEX) station datasets. Experimental results show that multi-GNSS/RNSS can guarantee plenty of visible satellites effectively. Compared with single-system GPS, PDOP, HDOP, and VDOP values of the multi-GNSS/RNSS are improved by 46.8%, 46.5% and 46.3%, respectively. As for convergence time, the static and kinematic PPP of multi-GNSS/RNSS are superior to that of the single-system GPS, whose reliability, availability, and stability drop sharply with the increasing elevation cutoff. At satellite elevation cutoff of 40 °, the single-system GPS fails to carry out continuous positioning because of the insufficient visible satellites, while the multi-GNSS/RNSS PPP can still get positioning solutions with relatively high accuracy, especially in the horizontal direction.

A Combined Homotopy Infeasible Interior-Point Method for Convex Nonlinear Programming

In this paper, on the basis of the logarithmic barrier function and KKT conditions , we propose a combined homotopy infeasible interior-point method (CHIIP) for convex nonlinear programming problems. For any convex nonlinear programming, without strict convexity for the logarithmic barrier function, we get different solutions of the convex programming in different cases by CHIIP method.

Penalized interior point approach for constrained nonlinear programming

A penalized interior point approach for constrained nonlinear programming is examined in this work.To overcome the difficulty of initialization for the interior point method,a problem equivalent to the primal problem via incorporating an auxiliary variable is constructed.A combined approach of logarithm barrier and quadratic penalty function is proposed to solve the problem.Based on Newton's method,the global convergence of interior point and line search algorithm is proven.Only a finite number of iterations is required to reach an approximate optimal solution.Numerical tests are given to show the effectiveness of the method.

The SCUSUM Estimation of Variance Change Point in Linear Process

这份报纸在线性过程考虑一个变化变化点的评价问题。一个 SCUSUM 类型变化点评估者的一致性被证明，它集中的率被建立。平均数未知的盒子也被考虑。

MHD stagnation point flow towards heated shrinking surface subjected to heat generation/absorption

The magnetohydrodynamic(MHD) stagnation point flow of micropolar fluids towards a heated shrinking surface is analyzed.The effects of viscous dissipation and internal heat generation/absorption are taken into account.Two explicit cases,i.e.,the prescribed surface temperature(PST) and the prescribed heat flux(PHF),are discussed.The boundary layer flow and energy equations are solved by employing the homotopy analysis method.The quantities of physical interest are examined through the presentation of plots/tabulated values.It is noticed that the existence of the solutions for high shrinking parameters is associated closely with the applied magnetic field.