A MODIFIED FRANK-WOLFE ALGORITHM AND ITS CONVERGENCE PROPERTIES

This paper modifies the Frank-Wolfe's algorithm. Under weaker conditions it proves that the modified algorithm is convergent, and specially under the assumption of convexity of the objective function that without assuming {x￣k} is bounded.

CONVERGENCE PROPERTIES OF THE DEPENDENT PRP CONJUGATE GRADIENT METHODS

In this paper, a new region of βk with respect to ;βk^PRP is given. With two Armijo-type line searches, the authors investigate the global convergence properties of the dependent PRP conjugate gradient methods, which extend the global convergence results of PRP conjugate gradient method proved by Grippo and Lucidi （1997） and Dai and Yuan （2002）.

Convergence Analysis and Its Application in the Fixed Point Formulation of Medium Access in Wireless Network

In the Internet of things, it is of critical importance to fully utilize the potential capacity of the network with efficient medium access control （MAC） mechanisms. In this paper, we study the convergence property of the fixed point formulation of distributed coordination function （DCF）, which is widely used for medium access control in wireless networks. We first Kind that the fixed point could be repelling, which means that it is impossible for an MAC system to converge at its fixed point. Next, we show the existence of periodic points to prove that the fixed point function will oscillate between two periodic points when the fixed point is repelling. We also find that the average of the two periodic points is a close approximation of the fixed point. Based on the findings, we propose an algorithm to compute the fixed point efficiently. Simulation results verify the accuracy and efficiency of our algorithm compared with the previous fixed point computing method.

A Relaxed Greedy Block Kaczmarz Method for Solving Large Consistent Linear Systems

Many problems in science and engineering require solving large consistent linear systems. This paper presents a relaxed greedy block Kaczmarz method (RGBK) and an accelerated greedy block Kaczmarz method (AGBK) for solving large-size consistent linear systems. The RGBK algorithm extends the greedy block Kaczmarz algorithm (GBK) presented by Niu and Zheng in [1] by introducing a relaxation parameter to the iteration formulation of GBK, and the AGBK algorithm uses different iterative update rules to minimize the running time. The convergence of the RGBK is proved and a method to determine an optimal parameter is provided. Several examples are presented to show the effectiveness of the proposed methods for overdetermined and underdetermined consistent linear systems with dense and sparse coefficient matrix.

Parallel EOI algorithm with different insertion schemes

A parallel embedding overlapped iterative (EOI) algorithm about classicimplicit equations with asymmetric Saul'yev schemes (CIS-EOI) to solve one-dimensional diffusionequations is discussed to improve the properties of the segment classic implicit iterative (SCII)algorithm. The structure of CIS-EOI method is given and the stability of scheme and convergence ofiteration are proved by matrix method. The property of gradual-approach convergence is alsodiscussed. It has been shown that the convergent rate is faster and the property of gradual-approachconvergence also becomes better with the increasing of the net point in subsystems than with theSCII algorithm. The simulation examples show that the parallel iterative algorithm with a differentinsertion scheme CIS-EOI is more effective.

Do Search and Selection Operators Play Important Roles in Multi-Objective Evolutionary Algorithms:A Case Study

Multi-objective Evolutionary Algorithm (MOEA) is becoming a hot research area and quite a few aspects of MOEAs have been studied and discussed. However there are still few literatures discussing the roles of search and selection operators in MOEAs. This paper studied their roles by solving a case of discrete Multi-objective Optimization Problem (MOP): Multi-objective TSP with a new MOEA. In the new MOEA, We adopt an efficient search operator, which has the properties of both crossover and mutation, to generate the new individuals and chose two selection operators: Family Competition and Population Competition with probabilities to realize selection. The simulation experiments showed that this new MOEA could get good uniform solutions representing the Pareto Front and outperformed SPEA in almost every simulation run on this problem. Furthermore, we analyzed its convergence property using finite Markov chain and proved that it could converge to Pareto Front with probability 1. We also find that the convergence property of MOEAs has much relationship with search and selection operators.

A method of recovering the initial vectors of globally coupled map lattices based on symbolic dynamics

Based on symbolic dynamics, a novel computationally efficient algorithm is proposed to estimate the unknown initial vectors of globally coupled map lattices （CMLs）. It is proved that not all inverse chaotic mapping functions are satisfied for contraction mapping. It is found that the values in phase space do not always converge on their initial values with respect to sufficient backward iteration of the symbolic vectors in terms of global convergence or divergence （CD）. Both CD property and the coupling strength are directly related to the mapping function of the existing CML. Furthermore, the CD properties of Logistic, Bernoulli, and Tent chaotic mapping functions are investigated and compared. Various simulation results and the performances of the initial vector estimation with different signal-to- noise ratios （SNRs） are also provided to confirm the proposed algorithm. Finally, based on the spatiotemporal chaotic characteristics of the CML, the conditions of estimating the initial vectors usiug symbolic dynamics are discussed. The presented method provides both theoretical and experimental results for better understanding and characterizing the behaviours of spatiotemporal chaotic systems.

Accelerated RHSS Iteration Method for Stabilized Saddle-Point Problems

For stabilized saddle-point problems, we apply the two iteration parameters idea for regularized Hermitian and skew-Hermitian splitting (RHSS) method and establish accelerated RHSS (ARHSS) iteration method. Theoretical analysis shows that the ARHSS method converges unconditionally to the unique solution of the saddle point problem. Finally, we use a numerical example to confirm the effectiveness of the method.

Uniform and L-convergence of Logarithmic Means of Walsh-Fourier Series

The （NSrlund） logarithmic means of the Fourier series of the integrable function f is：1/lnn-1∑k=1Sk（f）/n-k, where ln：=n-1∑k=11/k.In this paper we discuss some convergence and divergence properties of this logarithmic means of the Walsh-Fourier series of functions in the uniform, and in the L^1 Lebesgue norm. Among others, as an application of our divergence results we give a negative answer to a question of Móricz concerning the convergence of logarithmic means in norm.

Performance analysis of stochastic gradient algorithms under weak conditions

By using the stochastic martingale theory, convergence properties of stochastic gradient （SG） identification algorithms are studied under weak conditions. The analysis indicates that the parameter estimates by the SG algorithms consistently converge to the true parameters, as long as the information vector is persistently exciting （i.e., the data product moment matrix has a bounded condition number） and that the process noises are zero mean and uncorrelated. These results remove the strict assumptions, made in existing references, that the noise variances and high-order moments exist, and the processes are stationary and ergodic and the strong persis- tent excitation condition holds. This contribution greatly relaxes the convergence conditions of stochastic gradient algorithms. The simulation results with bounded and unbounded noise variances confirm the convergence conclusions proposed.

Inexact Operator Splitting Method for Monotone Inclusion Problems

The Douglas–Peaceman–Rachford–Varga operator splitting methods are a class ofefficient methods for finding a zero of the sum of two maximal monotone operatorsin a real Hilbert space;however, they are sometimes difficult or even impossible tosolve the subproblems exactly. In this paper, we suggest an inexact version in whichsome relative error criterion is discussed. The corresponding convergence propertiesare established, and some preliminary numerical experiments are reported to illustrateits efficiency.

PARALLEL CHAOTIC MULTISPLITTING ITERATIVE METHODS FOR THE LARGE SPARSE LINEAR COMPLEMENTARITY PROBLEM

Focuses on a study which presented a parallel chaotic multisplitting method for solving the large sparse linear complementarity problem. Preliminaries of the study; Equations of the parallel chaotic multisplitting method; Information on the convergence theories; Details on the parallel chaotic multisplitting relaxation methods.