Pi-sigma神经网络的带动量项的异步批处理梯度算法收敛性

本文将动量项引入到训练Pi-sigma神经网络的异步批处理的梯度算法中,有效的改善了算法的收敛效率,并从理论上对该算法的收敛性进行研究,给出了误差函数的单调性定理及该算法的弱收敛和强收敛性定理.计算机仿真实验亦验证了带动量项的异步批处理梯度算法的有效性和理论分析的正确性.     

Longtime Behaviour of Stochastic Hamiltonian Systems: The Multidimensional Case

Hamiltonian systems perturbed by a white noise force are discussed in several dimensions. By using an appropriate scaling of the stochastic force a convergence theorem for the invariants of the deterministic motion is proved. This corresponds to convergence of the system to a stationary distribution. Especially motion in a central force field is considered; the energy and angular momentum processes are investigated.     

On the approximation of square-integrable functions by exponential series

The expansion of a real square-integrable function in a Legendre series is considered. Existence of best approximations from different sets of exponential functions and their mean convergence to the function in question are proved. As an extension of this result existence and mean convergence of some non-linear best approximations that have been developed by Longman are also demonstrated.     

混合互补问题的光滑算法及收敛性

利用Fischer-Burmeister函数将混合互补问题转化为非线性方程组,由光滑函数逼近FB函数来求解非线性方程组．文中将信赖域方法和梯度法相结合,提出了Jacobian光滑化方法．算法在一定条件下的全局收敛性得到了证明,数值试验表明算法切实有效,有一定的优越性．     

线性l1模极小化问题的熵函数延拓法

本文通过利用极大熵函数构造同伦映射，建立了求解无约束线性l1模问题的熵函数延拓算法，证明了方法的收敛性，并给出了数值算例．     

A Dual Algorithm for Minimizing a Quadratic Function with Two Quadratic Constraints

In this paper, we present a dual algorithm for minimizing a convex quadratic function with two quadratic constraints. Such a minimization problem is a subproblem that appears in some trust region algorithms for general nonlinear programming. Some theoretical properties of the dual problem are given. Global convergence of the algorithm is proved and a local superlinear convergence result is presented. Numerical examples are also provided.     

The relaxation-time limit in the compressible Euler–Maxwell equations

The aim of this paper is to study multidimensional Euler–Maxwell equations for plasmas with short momentum relaxation time. The convergence for the smooth solutions to the compressible Euler–Maxwell equations toward the solutions to the smooth solutions to the drift–diffusion equations is proved by means of the Maxwell iteration, as the relaxation time tends to zero. Meanwhile, the formal derivation of the latter from the former is justified.     

Derivative-free simulated annealing and deflecting function technique for global optimization

A hybrid descent method based on simulated annealing (SA) algorithm and one modifying function technique, named deflecting function method, for global optimization is proposed. Unlike some previously proposed algorithms, the designed SA algorithm is executed repeatedly on the transformed function with respect to one prior-obtained local minimum instead of on the original objective function. Meanwhile, large scale searches at the beginning stages and small scale detections in the last stages are adopted. The global convergence is proved. Simulation demonstrates that the new method utilizes the obtained information effectively, so the convergence is significantly sped up and the success rate is greatly improved, compared with other existing methods. As an experimental result, how to combine SA and the deflecting function technique can make the new method more effective is discussed.     

Algorithm of Barrier Objective Penalty Function

In this paper, an algorithm of barrier objective penalty function for inequality constrained optimization is studied and a conception–the stability of barrier objective penalty function is presented. It is proved that an approximate optimal solution may be obtained by solving a barrier objective penalty function for inequality constrained optimization problem when the barrier objective penalty function is stable. Under some conditions, the stability of barrier objective penalty function is proved for convex programming. Specially, the logarithmic barrier function of convex programming is stable. Based on the barrier objective penalty function, an algorithm is developed for finding an approximate optimal solution to an inequality constrained optimization problem and its convergence is also proved under some conditions. Finally, numerical experiments show that the barrier objective penalty function algorithm has better convergence than the classical barrier function algorithm.     

多元q-Stancu多项式的收敛性及其收敛阶刻画

定义单纯形上的多元q-Stancu多项式,它是著名的Bernstein多项式,q-Bernstein多项式,Stancu多项式的推广.以多元函数的部分连续模及全连续模为度量,建立推广的多元q-Stancu多项式对连续函数的一致收敛定理与收敛阶估计,并以实例加以验证.     

ON THE CONVERGENCE OF AN APPROXIMATE PROXIMAL METHOD FOR DC FUNCTIONS

In this paper we prove the convergence of the approximate proximal method for DC functions proposed by Sun et al [6]. Our analysis also permits to treat the exact method. We then propose an interesting result in the case where the second component of the DC function is differentiable and provide some computational experiences which proved the efficiency of our method.     

Feynman integrals ofp-adic argument in the momentum space. I. Convergence

The regions of convergence of Feynman integrals ofp-adic arguments in the coordinate and momentum spaces are established, and a theorem on the Fourier transformation of Feynman amplitudes is proved.State University, Kazan. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 102, No. 3, pp. 367–377, March, 1995.     

加快迭代收敛速度的两个命题

定义了单调收敛函数和交错收敛函数,并根据其收敛特点,提出并证明了加快其收敛速度的两个命题.算例表明其效果较好.     

Convergence of estimated option price in a regime switching market

In an observed semi-Markov regime, estimation of transition rate of regime switching leads towards calculation of locally risk minimizing option price. Despite the uniform convergence of estimated step function of transition rate, to meet the existence of classical solution of the modified price equation, the estimator is approximated in the class of smooth functions and furthermore, the convergence is established. Later, the existence of the solution of the modified price equation is verified and the point-wise convergence of such approximation of option price is proved to answer the tractability of its application in Finance. To demonstrate the consistency in result a numerical experiment has been reported.     

Preservation of the convergence of trajectories under small perturbations of hyperbolic mappings of manifolds with boundary

A theorem is proved regarding the preservation of the convergence of trajectories under small perturbations of hyperbolic mappings, possessing a strict Lyapunov function. This result is applied to some models in population genetics.Translated from Teoriya Funktsii, Funktsional'nyi Analiz i Ikh Prilozheniya, No. 50, pp. 82–86, 1988.     

On the Cegrell classes

The Cegrell classes with zero boundary data are defined by certain decreasing approximating sequences of functions with different properties depending on the class in question. It is different for Cegrell classes which are given by a continuous function f, these classes are defined by an inequality. It is proved in this article that it is possible to define the Cegrell classes which are given by f in a similar manner as those classes with zero boundary data. An existence result for the Dirichlet problem for certain singular measures is proved. The article ends with three applications. Results connected to convergence in capacity, subextension of plurisubharmonic functions and integrability are proved.     

伪Newton—B族的导出及其性质

本文对无约束优化问题提出了一类新的近似牛顿法（伪牛顿-B族）,此方法同样具有二次终止性,产生的矩阵序列保持正定对称传递性。并证明了算法的全局收敛性和超级性收敛性。     

A trust region algorithm for equality constrained optimization

A trust region algorithm for equality constrained optimization is proposed that employs a differentiable exact penalty function. Under certain conditions global convergence and local superlinear convergence results are proved.     

CONVERGENCE PROPERTIES OF MULTI-DIRECTIONAL PARALLEL ALGORITHMS FOR UNCONSTRAINED MINIMIZATION

Convergence properties of a class of multi-directional parallel quasi-Newton algorithmsfor the solution of unconstrained minimization problems are studied in this paper.At eachiteration these algorithms generate several different quasi-Newton directions,and thenapply line searches to determine step lengths along each direction,simultaneously.Thenext iterate is obtained among these trail points by choosing the lowest point in the sense offunction reductions.Different quasi-Newton updating formulas from the Broyden familyare used to generate a main sequence of Hessian matrix approximations.Based on theBFGS and the modified BFGS updating formulas,the global and superlinear convergenceresults are proved.It is observed that all the quasi-Newton directions asymptoticallyapproach the Newton direction in both direction and length when the iterate sequenceconverges to a local minimum of the objective function,and hence the result of superlinearconvergence follows.     

Exactness and algorithm of an objective penalty function

Penalty function is an important tool in solving many constrained optimization problems in areas such as industrial design and management. In this paper, we study exactness and algorithm of an objective penalty function for inequality constrained optimization. In terms of exactness, this objective penalty function is at least as good as traditional exact penalty functions. Especially, in the case of a global solution, the exactness of the proposed objective penalty function shows a significant advantage. The sufficient and necessary stability condition used to determine whether the objective penalty function is exact for a global solution is proved. Based on the objective penalty function, an algorithm is developed for finding a global solution to an inequality constrained optimization problem and its global convergence is also proved under some conditions. Furthermore, the sufficient and necessary calmness condition on the exactness of the objective penalty function is proved for a local solution. An algorithm is presented in the paper in finding a local solution, with its convergence proved under some conditions. Finally, numerical experiments show that a satisfactory approximate optimal solution can be obtained by the proposed algorithm.