Criteria for strong H-tensors

H-tensor is a new developed concept which plays an important role in tensor analysis and computing. In this paper, we explore the properties of H-tensors and establish some new criteria for strong H-tensors. In particular, based on the principal subtensor, we provide a new necessary and sufficient condition of strong H-tensors, and based on a type of generalized diagonal product dominance, we establish some new criteria for identifying strong H-tensors. The results obtained in this paper extend the corresponding conclusions for strong H-matrices and improve the existing results for strong H-tensors.     

A primal-dual interior-point algorithm for symmetric optimization based on a new method for finding search directions

We introduce an interior-point method for symmetric optimization based on a new method for determining search directions. In order to accomplish this, we use a new equivalent algebraic transformation on the centring equation of the system which characterizes the central path. In this way, we obtain a new class of directions. We analyse a special case of this class, which leads to the new interior-point algorithm mentioned before. Another way to find the search directions is using barriers derived from kernel functions. We show that in our case the corresponding direction cannot be deduced from a usual kernel function. In spite of this fact, we prove the polynomial complexity of the proposed algorithm.     

Banach空间中关于(H,η)-增生算子的一类新变分包含组问题

In this paper,we first introduce a new class of generalized accretive operators named(H,η)-accretive in Banach space.By studying the properties of(H,η)-accretive,we extend the concept of resolvent operators associated with m-accretive operators to the new(H,η)-accretive operators.In terms of the new resolvent operator technique,we prove the existence and uniqueness of solutions for this new system of variational inclusions.We also construct a new algorithm for approximating the solution of this system and discuss the convergence of the sequence of iterates generated by the algorithm.     

Hilbert空间中关于松弛协强制映射的一类新的广义变分不等式组

在本文中,我们首先引入了一类新的关于松弛协强制映射的广义变分不等式组,通过用度量投影的方法,我们证明了这类广义变分不等式组解的存在性和唯一性.我们也建立了一类新的算法来逼近这一不等式组的解,本文的结果使得近期相关结果成为本文的特殊情况.     

Minimizing the passengers’ traveling time in the stop location problem

In this paper we consider the location of stops along the edges of an already existing public transportation network. The positive effect of new stops is given by the better access of the passengers to the public transport network, while the passengers’ traveling time increases due to the additional stopping activities of the trains, which is a negative effect for the passengers. The problem has been treated in the literature where the most common model is to cover all demand points with a minimal number of new stops. In this paper, we follow this line and seek for a set of new stops covering all demand points but instead of minimizing the number of new stops we minimize the additional passengers’ traveling time due to the new stops. For computing this additional traveling time we do not only take the stopping times of the vehicles but also acceleration and deceleration of the vehicles into account. We show that the problem is NP-hard, but we are able to derive a finite candidate set and two tractable IP formulations. For linear networks we show that the problem is polynomially solvable. We also discuss the differences to the common models from literature showing that minimizing the number of new stops does not necessarily lead to a solution with minimal additional traveling times for the passengers. We finally provide a case study showing that our new model decreases the traveling times for the passengers while still achieving the minimal number of new stops.     

On practical asymptotic stabilizability of switched affine systems

In this paper, we report some new results on practical asymptotic stabilizability of switched systems consisting of affine subsystems. We first briefly review some practical asymptotic stabilizability notions and some results from our previous papers. Then we propose a new approach to estimate the region of attraction for switched affine systems. Based on this new approach, we present several new sufficient conditions for the practical asymptotic stabilizability and global practical asymptotic stabilizability of such systems. Finally, a computational approach to check the new sufficient conditions is proposed and it is applied to several numerical examples.     

Contraction of the proximal mapping and applications to the equilibrium problem

In this paper, we introduce a new definition of Lipschitz-type continuity of a bifunction. Using this definition, we prove the contraction of the proximal mapping and apply it to the equilibrium problem over the fixed-point set of a nonexpansive mapping. We present a new algorithm for this problem. Under classical conditions, the convergence of the algorithm is proved. Finally, we present some numerical results for the proposed algorithm.     

Strong convergence theorem by shrinking projection method for new nonlinear mappings in Banach spaces and applications

In this paper, we introduce the concept of a new nonlinear mapping called demigeneralized in a Banach space. Then, using the shrinking projection method, we prove a strong convergence theorem for finding a common fixed point for a family of the new nonlinear mappings in a Banach space. We apply this result to obtain new strong convergence theorems in a Hilbert space and a Banach space, respectively.     

Computing all solutions to polynomial systems using homotopy continuation

In a previous paper we described a new method for defining homotopies for finding all solutions to polynomial systems. A major feature of this new approach is that the start system for the homotopy need not be a “random” or “generic” system. Also, homotopy paths are strictly increasing in the homotopy parameter. In this paper we establish some principles of implementation and report on the performance of programs that use the new homotopies. A feature of our implementation is that we eliminate divergent paths entirely. We include performance statistics for homotopies derived from more traditional approaches for comparison. Generally, the new approach is faster and more reliable.     

On the univalence of an integral operator defined by Hadamard product

In this paper, we introduce a new general integral operator defined by the Hadamard product. Furthermore, we obtained new sufficient conditions for this operator to be univalent in the open unit disk.     

Projection algorithms for solving a system of general variational inequalities

In this paper, we introduce and consider a new system of general variational inequalities involving four different operators. Using the projection operator technique, we suggest and analyze some new explicit iterative methods for this system of variational inequalities. We also study the convergence analysis of the new iterative method under certain mild conditions. Since this new system includes the system of variational inequalities involving three operators, variational inequalities and related optimization problems as special cases, results obtained in this paper continue to hold for these problems. Our results can be viewed as a refinement and improvement of the previously known results for variational inequalities.     

H-单调映象的广义Fuzzy隐拟变分包含

引入了一类H-单调映象的广义Fuzzy隐拟变分包含问题,利用文[1]中H-单调映象的预解算子技巧研究了这类变分包含解的迭代算法逼近,证明了其解的存在性以及由算法生成的迭代序列的收敛性。     

A new nonmonotone line search technique for unconstrained optimization

In this paper, we propose a new nonmonotone line search technique for unconstrained optimization problems. By using this new technique, we establish the global convergence under conditions weaker than those of the existed nonmonotone line search techniques.     

ON POLYNOMIAL AUTOMORPHISM IDENTITY SETS AND IDENTITY POLYNOMIALS

In this paper, we propose a new condition for hypersurfaces to be polynomial automorphism identity sets. This new condition can be used to give a new proof of Mckay-Wang's problem. Moreover, we also study the concepts of identity polynomials, and give a criterion for a polynomial to be identity polynomial.     

Matrix free MEBDF method for the solution of stiff systems of ODEs

In this paper, we present the details of a new method which is a hybrid method of MF-BDF and MEBDF. To obtain this new method which we call MF-MEBDF, we compose the matrix free properties of the first method and the accuracy of MEBDF, elaborately. Application of this new method to some important stiff problems show that MF-MEBDF is generally faster than MEBDF and more accurate than MF-BDF and MEBDF. Since in MEBDF, the LU factorization is used, we expect MF-MEBDF to be more efficient than the other two methods for large stiff systems of ODEs.     

Banach空间中含$(H,\eta)$单调算子变分包含组解的迭代法

In this paper, we introduce and study a new system of variational inclusions involving （H, η）-monotone operators in Banach space. Using the resolveut operator associated with （H, η）- monotone operators, we prove the existence and uniqueness of solutions for this new system of variational inclusions. We also construct a new algorithm for approximating the solution of this system and discuss the convergence of the iterative sequence generated by the algorithm.     

Convergence of quasi-Newton method with new inexact line search

Quasi-Newton method is a well-known effective method for solving optimization problems. Since it is a line search method, which needs a line search procedure after determining a search direction at each iteration, we must decide a line search rule to choose a step size along a search direction. In this paper, we propose a new inexact line search rule for quasi-Newton method and establish some global convergent results of this method. These results are useful in designing new quasi-Newton methods. Moreover, we analyze the convergence rate of quasi-Newton method with the new line search rule.     

广义多值拟变分包含解的两步迭代

本文引入并研究了Hilbert空间中的一类广义多值拟变分包含问题.借助预解算子技巧构造了一个新的两步迭代算法来逼近广义多值拟变分包含的解,并且证明了其解的存在性以及迭代算法生成的迭代序列的收敛性.     

Baskakov算子加权逼近的收敛阶

本文讨论了Ｂａｓｋａｋｏｖ算子加Ｊａｃｏｂｉ权逼近的收敛性，首先指出了按通常的加权范数，Ｂａｓｋａｋｏｖ算子是无界的。然后引入一种新的范数，在此范数下Ｂａｓｋａｋｏｖ算子具有压缩性，最后借助于Ｋ－泛函，我们着重讨论了它的特征刻划问题。