BANDWIDTH SELECTION IN NONPARAMETRIC SPECTRAL DENSITY ESTIMATION OF THE STATIONARY GAUSSIAN PROCESS

ＢＡＮＤＷＩＤＴＨＳＥＬＥＣＴＩＯＮＩＮＮＯＮＰＡＲＡＭＥＴＲＩＣＳＰＥＣＴＲＡＬＤＥＮＳＩＴＹＥＳＴＩＭＡＴＩＯＮＯＦＴＨＥＳＴＡＴＩＯＮＡＲＹＧＡＵＳＳＩＡＮＰＲＯＣＥＳＳ￥ＹＵＤＡＮ（于丹）（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅ，...     

广义非线性互补问题的投影收缩法

广义非线性互补问题的投影收缩法孙德锋（中国科学院应用数学研究所）ＡＰＲＯＪＥＣＴＩＯＮＡＮＤＣＯＮＴＲＡＣＴＩＯＮＭＥＴＨＯＤＦＯＲＴＨＥＮＯＮＬＩＮＥＡＲＣＯＭＰＬＥＭＥＮＴＡＲＩＴＹＰＲＯＢＬＥＭＡＮＤＩＴＳＥＸＴＥＮＳＩＯＮＳ￥ＳｕｎＤｅ－ｆｅ...     

TWO NEW CONSTRUCTIONS OF CARTESIAN AUTHENTICATION CODES FROM SYMPLECTIC GEOMETRY

ＴＷＯＮＥＷＣＯＮＳＴＲＵＣＴＩＯＮＳＯＦＣＡＲＴＥＳＩＡＮＡＵＴＨＥＮＴＩＣＡＴＩＯＮＣＯＤＥＳＦＲＯＭＳＹＭＰＬＥＣＴＩＣＧＥＯＭＥＴＲＹＧＡＯＹＯＵＡＮＤＺＯＵＺＥＮＧＪＩＡ（ＤｅｐａｒｔｍｅｎｔｏｆＢａｓｉｃＳｃｉｅｎｃｅ，Ｎｏｒｔｈｅａｓｔ...     

LARGE DEVIATIONS FOR INFINITE DIMENSIONAL AND REVERSIBLE REACTION－DIFFUSION PROCESSES

ＬＡＲＧＥＤＥＶＩＡＴＩＯＮＳＦＯＲＩＮＦＩＮＩＴＥＤＩＭＥＮＳＩＯＮＡＬＡＮＤＲＥＶＥＲＳＩＢＬＥＲＥＡＣＴＩＯＮ－ＤＩＦＦＵＳＩＯＮＰＲＯＣＥＳＳＥＳＣＨＥＮＪＩＮＷＥＮ（陈金文）（ＤｅｐｅｒｔｍｅｎｔｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，Ｔ...     

A SUFFICIENT CONDITION FOR NON－COEXISTENCE OF ONE DIMENSIONAL MULTICOLOR CONTACT PROCESSES

ＡＳＵＦＦＩＣＩＥＮＴＣＯＮＤＩＴＩＯＮＦＯＲＮＯＮ－ＣＯＥＸＩＳＴＥＮＣＥＯＦＯＮＥＤＩＭＥＮＳＩＯＮＡＬＭＵＬＴＩＣＯＬＯＲＣＯＮＴＡＣＴＰＲＯＣＥＳＳＥＳＬＩＵＸＩＵＦＡＮＧ（刘秀芳）ＷＡＮＧＪＵＮ（王军）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍ...     

ASYMPTOTIC BEHAVIOR OF NONOSCILLATORY SOLUTIONS OF A SECOND ORDER FUNCTIONAL DIFFERENTIAL EQUATIONS

ＡＳＹＭＰＴＯＴＩＣＢＥＨＡＶＩＯＲＯＦＮＯＮＯＳＣＩＬＬＡＴＯＲＹＳＯＬＵＴＩＯＮＳＯＦＡＳＥＣＯＮＤＯＲＤＥＲＦＵＮＣＴＩＯＮＡＬＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳ（孟繁伟）曲阜师范大学，邮编：２７３１６５ＭｅｎｇＦａｎｗｅｉ（ＱｕｆｕＮ...     

EXISTENCE AND GLOBAL ATTRACTIVITY OF PERIODIC SOLUTION OF A MODEL IN POPULATION DYNAMICS

ＥＸＩＳＴＥＮＣＥＡＮＤＧＬＯＢＡＬＡＴＴＲＡＣＴＩＶＩＴＹＯＦＰＥＲＩＯＤＩＣＳＯＬＵＴＩＯＮＯＦＡＭＯＤＥＬＩＮＰＯＰＵＬＡＴＩＯＮＤＹＮＡＭＩＣＳ￥ＷＥＮＧＰＥＩＸＵＡＮ（佩萱）ＬＩＡＮＧＭＩＡＯＬＩＡＮ（梁妙莲）（ＤｅｐａｒｔｍｅｎｔｏｆＳｏ...     

ON A PAIR OF NON-ISOMETRIC ISOSPECTRAL DOMAINS WITH FRACTAL BOUNDARIES AND THE WEYL-BERRY CONJECTURE

ＯＮＡＰＡＩＲＯＦＮＯＮＩＳＯＭＥＴＲＩＣＩＳＯＳＰＥＣＴＲＡＬＤＯＭＡＩＮＳＷＩＴＨＦＲＡＣＴＡＬＢＯＵＮＤＡＲＩＥＳＡＮＤＴＨＥＷＥＹＬＢＥＲＲＹＣＯＮＪＥＣＴＵＲＥＳＬＥＥＭＡＮ，Ｂ．Ｄ．ＣＨＥＮＨＵＡＭａｎｕｓｃｒｉｐｔｒｅｃ...     

BOOTSTRAP MAXIMUM LIKELIHOOD ESTIMATION OF THE PARAMETER IN SPECTRAL DENSITY OF STATIONARY PROCESSES

ＢＯＯＴＳＴＲＡＰ　ＭＡＸＩＭＵＭＬＩＫＥＬＩＨＯＯＤＥＳＴＩＭＡＴＩＯＮＯＦＴＨＥＰＡＲＡＭＥＴＥＲＩＮＳＰＥＣＴＲＡＬＤＥＮＳＩＴＹＯＦＳＴＡＴＩＯＮＡＲＹ　ＰＲＯＣＥＳＳＥＳＹＵＤＡＮ（于丹）（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅ...     

A NOTE OF UNIFORM EXPONENTIAL STABILIZATION FOR NONCONTRACTIVE SEMIGROUPS UNDER COMPACT PERTURBATION

ＡＮＯＴＥＯＦＵＮＩＦＯＲＭＥＸＰＯＮＥＮＴＩＡＬＳＴＡＢＩＬＩＺＡＴＩＯＮＦＯＲＮＯＮＣＯＮＴＲＡＣＴＩＶＥＳＥＭＩＧＲＯＵＰＳＵＮＤＥＲＣＯＭＰＡＣＴＰＥＲＴＵＲＢＡＴＩＯＮＳｏｎｇＧｕｏｚｈｕ（宋国柱）（Ｄｅｐｔ．ｏｆＭａｔｈ．，Ｎａｎｊｉｎｇ...     

Comparison of Two Kinds of Prediction-Correction Methods for Monotone Variational Inequalities

In this paper, we study the relationship between the forward-backward splitting method and the extra-gradient method for monotone variational inequalities. Both of the methods can be viewed as prediction-correction methods. The only difference is that they use different search directions in the correction-step. Our analysis explains theoretically why the extra-gradient methods usually outperform the forward-backward splitting methods. We suggest some modifications for the two methods and numerical results are given to verify the superiority of the modified methods.     

A COMPARISON OF DIFFERENT CONTRACTION METHODS FOR MONOTONE VARIATIONAL INEQUALITIES

It is interesting to compare the efficiency of two methods when their computational loads in each iteration are equal. In this paper, two classes of contraction methods for monotone variational inequalities are studied in a unified framework. The methods of both classes can be viewed as prediction-correction methods, which generate the same test vector in the prediction step and adopt the same step-size rule in the correction step. The only difference is that they use different search directions. The computational loads of each iteration of the different classes are equal. Our analysis explains theoretically why one class of the contraction methods usually outperforms the other class. It is demonstrated that many known methods belong to these two classes of methods. Finally, the presented numerical results demonstrate the validity of our analysis.     

A Differential Evolution algorithm to deal with box, linear and quadratic-convex constraints for boundary optimization

We both propose and test an implicit strategy that is based on changing the search space from points to directions, which in combination with the Differential Evolution (DE) algorithm, is easily implemented for solving boundary optimization of a generic continuous function. In particular, we see that the DE method can be efficiently implemented to find solutions on the boundary of a convex and bounded feasible set resulting when the constraints are bounds on the variables, linear inequalities and quadratic convex inequalities. The computational results are performed on different classes of boundary minimization problems. The proposed technique is compared with the Generalized Differential Evolution method.     

变分不等式与互补问题、双层规划与平衡约束数学规划问题的若干进展

考虑有限维变分不等式与互补问题、双层规划以及均衡约束的数学规划问题. 在简单介绍这些问题之后,重点介绍近年来这些领域中发展迅速的几个研究方向,包括对称锥互补问题的理论与算法、变分不等式的投影收缩算法、随机变分不等式与随机互补问题的模型与方法、双层规划以及均衡约束数学规划问题的新方法. 最后提出几个进一步研究的方向.     

A class of projection-contraction methods applied to monotone variational inequalities

First, an extension of the projection-contraction (PC) method is introduced, which generalizes a class of the existing PC methods, and then the extended projection-contraction (EPC) method is applied to the solvability of a class of general monotone variational inequalities.     

Hit-and-run algorithms for the identification of nonredundant linear inequalities

Two probabilistic hit-and-run algorithms are presented to detect nonredundant constraints in a full dimensional system of linear inequalities. The algorithms proceed by generating a random sequence of interior points whose limiting distribution is uniform, and by searching for a nonredundant constraint in the direction of a random vector from each point in the sequence. In the hypersphere directions algorithm the direction vector is drawn from a uniform distribution on a hypersphere. In the computationally superior coordinate directions algorithm a search is carried out along one of the coordinate vectors. The algorithms are terminated through the use of a Bayesian stopping rule. Computational experience with the algorithms and the stopping rule will be reported.     

A modified descent method for co-coercive variational inequalities

This paper presents a modified descent method for solving co-coercive variational inequalities. Incorporating with the techniques of identifying descent directions and optimal step sizes along these directions, the new method improves the efficiencies of some existing projection methods. Some numerical results for an economic equilibrium problem are reported.     

New Parallel Descent-like Method for Solving a Class of Variational Inequalities

To solve a class of variational inequalities with separable structures, some classical methods such as the augmented Lagrangian method and the alternating direction methods require solving two subvariational inequalities at each iteration. The most recent work (B.S. He in Comput. Optim. Appl. 42(2):195–212, 2009) improved these classical methods by allowing the subvariational inequalities arising at each iteration to be solved in parallel, at the price of executing an additional descent step. This paper aims at developing this strategy further by refining the descent directions in the descent steps, while preserving the practical characteristics suitable for parallel computing. Convergence of the new parallel descent-like method is proved under the same mild assumptions on the problem data.     

结合修正Curry-Altman步长搜索一个新的共轭梯度算法的收敛性

Conjugate gradient optimization algorithms depend on the search directions with different choices for the parameter in the search directions. In this note, conditions are given on the parameter in the conjugate gradient directions to ensure the descent property of the search directions. Global convergence of such a class of methods is discussed. It is shown that, using reverse modulus of continuity function and forcing function, the new method for solving unconstrained optimization can work for a continuously differentiable function with a modification of the Curry-Altman‘s step-size rule and a bounded level set. Combining PR method with our new method, PR method is modified to have global convergence property.Numerical experiments show that the new methods are efficient by comparing with FR conjugate gradient method.     

Randomized search directions in descent methods for minimizing certain quasidifferentiable functions

Several descent methods have recently been proposed for minimizing smooth compositions of max-type functions. The methods generate many search directions at each iteration. This paper shows that a random choice of only two search directions at each iteration suffices for retaining convergence to inf-stationary points with probability 1. This technique may decrease significantly the work in quadratic programming and line searches, thus enabling efficient implementations of the methods.