COMPLETELY BOUNDED COHOMOLOGY OF NON-SELFADJOINT OPERATOR ALGEBRAS

The authors prove that all n-th completely bounded cohomology groups of a nest algebra T（N） acting on a separable Hilbert space are trivial when the coefficients lie in any ultraweakly closed T（N）-bimodule containing the nest algebra. They also prove that Hcb^n（A, M） ≌ Hcb^n（A, M） for all n ≥ 1 and a CSL algebra .A with an ultraweakly closed .A-bimodul.M containing A.

Control of group of mobile autonomous agents via local strategies

This paper considers the formation control problem of multi-agent systems in a distributed fashion. Two cases of the information propagating topologies among multiple agents, characterized by graphics model, are considered. One is fixed topology. The other is switching topology which represents the limited and less reliable information exchange. The local formation control strategies established in this paper are based on a simple modification of the existing consensus control strategies. Moreover, some existing convergence conditions are shown to be a special case of our model even in the continuous-time consensus case. Therefore, the results of this paper extend the existing results about the consensus problem.

The Rate of Convergence of Augmented Lagrangian Method for Minimax Optimization Problems with Equality Constraints

The augmented Lagrangian function and the corresponding augmented Lagrangian method are constructed for solving a class of minimax optimization problems with equality constraints.We prove that,under the linear independence constraint qualification and the second-order sufficiency optimality condition for the lower level problem and the second-order sufficiency optimality condition for the minimax problem,for a given multiplier vectorμ,the rate of convergence of the augmented Lagrangian method is linear with respect to||μu-μ^(*)||and the ratio constant is proportional to 1/c when the ratio|μ-μ^(*)||/c is small enough,where c is the penalty parameter that exceeds a threshold c_(*)>O andμ^(*)is the multiplier corresponding to a local minimizer.Moreover,we prove that the sequence of multiplier vectors generated by the augmented Lagrangian method has at least Q-linear convergence if the sequence of penalty parameters(ck)is bounded and the convergence rate is superlinear if(ck)is increasing to infinity.Finally,we use a direct way to establish the rate of convergence of the augmented Lagrangian method for the minimax problem with a quadratic objective function and linear equality constraints.

A NEW GRADIENT PROJECTION METHOD AND ITS CONVERGENCE

In this paper, by using a new projection, we construct a variant of Zhang’s algorithm and prove its convergence. Specially, the variant of Zhang’s algorithm has quadratic termination and superlinear convergence rale under certain conditions. Zhang’s algorithm hasn’t these properties.

A REGULARIZATION NEWTON METHOD FOR MIXED COMPLEMENTARITY PROBLEMS

In this paper, a regularization Newton method for mixed complementarity problem(MCP) based on the reformulation of MCP in [1] is proposed. Its global convergence is proved under the assumption that F is a P0-function. The main feature of our algorithm is that a priori of the existence of an accumulation point for convergence need not to be assumed.

广义半无限规划新的最优性条件(英文)

本文讨论了一类指标集依赖于决策变量的广义半无限规划(GSMMP).首先通过刻画目标函数的Clarke导数和Clarke次微分,建立其一阶最优性条件.其次,通过对下层问题Q(X)进行扰动分析,我们得到Q(X)的一个精确罚表示.由此,利用一组精确罚函数将(GSMMP)转化为经典的半无限极大极小规划,从而可利用已有的经典半无限规划的算法来对(GSMMP)进行求解.

Banach Limits Revisited

Order unit normed linear spaces are a special type of regularly ordered normed linear spaces and therefore the first section is a short collection of the fundamental results on this type of normed linear spaces. The connection between order unit normed linear spaces and base normed linear spaces within the category of regularly ordered normed linear spaces is described in Section 2, and Section 3 at last, contains the results on Banach limits in an arbitrary order unit normed linear space. It is shown that the original results on Banach limits are valid for a greater range.

ON-LINE SCHEDULING OF UNIT TIME JOBS WITH REJECTION ON UNIFORM MACHINES

作者考虑与拒绝惩罚在一致机器上统一实行时间工作的联机安排的问题。这些工作一个一个地到达；能任何一个被接受；安排，或被拒绝。目的是最小化接受工作的全部的结束时间；拒绝工作的全部的惩罚。作者建议一个联机算法；证明竞争比率。

A UNIFIED ALGORITHMIC FRAMEWORK OF SYMMETRIC GAUSS-SEIDEL DECOMPOSITION BASED PROXIMAL ADMMS FOR CONVEX COMPOSITE PROGRAMMING

This paper aims to present a fairly accessible generalization of several symmetric Gauss-Seidel decomposition based multi-block proximal alt ernating direction met hods of multipliers(ADMMs)for convex composite optimization problems.The proposed method unifies and refines many constructive techniques that were separately developed for the computational efficiency of multi-block ADMM-type algor计hms.Specifically,the majorized augmented Lagrangian functions,the indefinite proximal terms,the inexact symmetrie Gauss-Seidel decomposition theorem,the tolerance criteria of approximately solving the subproblems,and the large dual step-lengths,are all incorporated in one algoi?计hmic framework,which we named as sGS-imiPADMM.From the popularity of convergent variants of multi-block ADMMs in recent years,especially for high-dimensional multi-block convex composite conic programming problems,the unification presen ted in this paper,as well as the corresponding convergence results,may have the great potential of facilitating the implemen tation of many multi-block ADMMs in various problem set tings.

Multi-objective optimization of environmental tax for mitigating air pollution and greenhouse gas

Government macro-control through various policies is an important way to mitigate air pollution and greenhouse gases.Therefore,environmental tax is used worldwide as an important measure.However,few studies have considered the interaction between carbon and environmental protection taxes.Additionally,different sectors differ in their energy structure,pollution emission intensity,and economic status,and previous studies rarely proposed differentiated environmental tax rates based at the sectoral level.A model framework combining the computable general equilibrium(CGE)model and Bayesian optimization(BO)algorithm is proposed to maximize GDP,meet environmental planning objectives,and explore the optimal environmental taxation scheme to realize the multi-objective optimization of the economy and environment.Meanwhile,this study compares the different impact mechanisms of environmental protection tax and carbon tax.It discusses the impacts of differentiated environmental tax rates in different sectors on the environment and economy.For example,the results show that the coordinated implementation of environmental protection and carbon tax policies and the sectoral differentiated environmental tax rates in China could better balance economic development and environmental governance.Additionally,the optimal taxation scheme could mitigate air pollution and greenhouse gases,promote economic growth,and realize sustainable economic and environmental development.Furthermore,the optimized taxation scheme positively affects the energy and industrial structures.

ONE LIMIT THEOREM, OPTIMAL CRITERION AND EXISTENCE THEOREM OF THE DUAL NONLINEAR PROGRAM

R. T. Rockafellar built a new general convex dual theory by introducing the conjugate function and the perturbation function. Following him, many other authors obtained some important results in generalized convex dual programs and

On Several Results of Chandrasekaran-Tamir Conjecture

Fermat-Weber location problem may be described

GLOBAL CONVERGENCE OF A CLASS OF SMOOTH PENALTY METHODS FOR SEMI-INFINITE PROGRAMMING

为半无限的编程(啜) 问题，作者首先由使用积分与一仅仅不平等限制把它变换成一个相等的非线性的编程问题工作，然后基于光滑的函数的一个类建议一个光滑的惩罚方法。这个方法的主要特征是惩罚功能的全球答案未必在每次重复被解决，并且在温和假设下面，当不可分的功能的评估不是很昂贵的时，方法总是可行、有效。全球集中性质当任何限制资格不在时被获得，也就是说，算法产生的顺序的任何累积点是 SIP 的答案。而且，作者显示出方法的一条不安定理并且获得几有趣的结果。而且，作者证明所有反复的点在 Mangasarian-Fromovitz 限制资格下面在重复的一个有限数字以后仍然保持可行。最后，数字结果被给。

GLOBAL CONVERGENCE OF THE DAI-YUAN CONJUGATE GRADIENT METHOD WITH PERTURBATIONS

在这篇论文，作者建议奶妈元的一个班(abbr。DY ) 在一般功能上面对不安与线搜索结合坡度方法；一致地凸的功能分别地。在主要方向 s k 被 DY 获得的地方，他们的 iterate 公式是 x k+1 = x k + α k (s k + ω k ) 结合坡度方法，ω k 是不安术语，；步尺寸α k 被不必然在限制趋于到零的线搜索决定。作者在温和条件下面证明这些方法的全球集中。初步的计算经验也被报导。

New Differential Properties of Sup-type Functions

In this paper, we study the directional derivative, subderivative, and subdifferential of sup-type functions without any compactness assumption on the index set. As applications, we provide an estimate of the Lipschitz modulus for sup-type functions.

ON THE CONVERGENCE OF A NEW HYBRID PROJECTION ALGORITHM

为非强迫的优化，一个新混合设计算法在纸被介绍。这个算法有一些吸引人的集中性质。Convergencetheory 能在▽ f (x) 是一致地连续的条件下面被获得。如果▽ f (x) 是连续地可辨的伪 convex，整个顺序重申没有任何另外的假设，收敛到这个问题的一个答案。而且，在适当条件下面，一个人证明顺序重申有一个簇点如果并且仅当Ω ~* ≠ 0。数字例子在这篇论文的结束被给。

On Some Aspects of Perturbation Analysis for Matrix Cone Optimization Induced by Spectral Norm

In this paper,we consider a cone problem of matrix optimization induced by spectral norm(MOSN).By Schur complement,MOSN can be reformulated as a nonlinear semidefinite programming(NLSDP)problem.Then we discuss the constraint nondegeneracy conditions and strong second-order sufficient conditions of MOSN and its SDP reformulation,and obtain that the constraint nondegeneracy condition of MOSN is not always equivalent to that of NLSDP.However,the strong second-order sufficient conditions of these two problems are equivalent without any assumption.Finally,a sufficient condition is given to ensure the nonsingularity of the Clarke’s generalized Jacobian of the KKT system for MOSN.

Dynamic Concept of Returns to Scales and Its Characteristics on Production Frontier in Intersection Form

This paper gives a dynamic concept and a new non-parametric method for evaluating returns to scale（RTS） of economic units with multiple inputs and outputs.It is frequently noticed that when we increase the input of a decision making unit（DMU） with a certain status of RTS,different status of RTS is observed.For example,when we increase the input of a DMU with constant RTS under the traditional method,a decreasing RTS is often observed instead of the expected constant RTS.We thus define the RTS of each DMU in both input expansion and contraction regions respectively.The research starts from transferring the production possibility set into the intersection form,by giving the explicit linear inequality representation of production frontiers.The RTS structural characteristics of DMUs＇ on the production frontier are described.Status of RTS of those DMUs on the production frontier include increasing RTS,constant RTS,decreasing RTS,saturated RTS and evidence of congestion.Necessary and suficient conditions for RTS evaluation are provided.The definition and evaluation method given here provide more detailed economic characteristics of DMU for policy makers.

Comparison of dimension reduction methods for DEA under big data via Monte Carlo simulation

Data with large dimensions will bring various problems to the application of data envelopment analysis(DEA).In this study,we focus on a“big data”problem related to the considerably large dimensions of the input-output data.The four most widely used approaches to guide dimension reduction in DEA are compared via Monte Carlo simulation,including principal component analysis(PCA-DEA),which is based on the idea of aggregating input and output,efficiency contribution measurement(ECM),average efficiency measure(AEC),and regression-based detection(RB),which is based on the idea of variable selection.We compare the performance of these methods under different scenarios and a brand-new comparison benchmark for the simulation test.In addition,we discuss the effect of initial variable selection in RB for the first time.Based on the results,we offer guidelines that are more reliable on how to choose an appropriate method.