Interior-Point Solver for Large-Scale Quadratic Programming Problems with Bound Constraints

In this paper, we present an interior-point algorithm for large and sparse convex quadratic programming problems with bound constraints. The algorithm is based on the potential reduction method and the use of iterative techniques to solve the linear system arising at each iteration. The global convergence properties of the potential reduction method are reassessed in order to take into account the inexact solution of the inner system. We describe the iterative solver, based on the conjugate gradient method with a limited-memory incomplete Cholesky factorization as preconditioner. Furthermore, we discuss some adaptive strategies for the fill-in and accuracy requirements that we use in solving the linear systems in order to avoid unnecessary inner iterations when the iterates are far from the solution. Finally, we present the results of numerical experiments carried out to verify the effectiveness of the proposed strategies. We consider randomly generated sparse problems without a special structure. Also, we compare the proposed algorithm with the MOSEK solver. Research partially supported by the MIUR FIRB Project RBNE01WBBB “Large-Scale Nonlinear Optimization.”     

A note on repeated games with non-monotonie value

We show that even when the information structure is independent of the state of nature, the value of then-stage zero-sum game with incomplete information is not necessarily monotonie with respect to the length of the game. More precisely, we give an example of such ann-stage game in whichV ₁ >V ₂ <V ₃.I am very grateful to Ehud Lehrer who introduced this question to me.     

Utility function assessment on a micro-computer: An interactive procedure

The procedure UFAP is presented which allows a decision maker to interactively assess his von Neumann/Morgenstern single attribute utility function. UFAP puts special emphasis on potential biases in the assessment process. In the first part of the procedure three different assessment methods are used to derive ranges for the utility function. Using different methods enables us to point out a possible bias in the elicitation process. In the second part a consistent class of utility functions is derived based on the ranges assessed in the first part. In case inconsistencies between methods arise the decision maker has to reconsider selected preference statements previously given.     

The design of a Tort law to control accidents

In this paper we analyse a two-stage game involving the government and n agents who engage in a single activity (driving). The government establishes the legal policy setting and the agents proceed to play a non-cooperative game of incomplete information with a risk of accident in which their behavioral strategy is their level of care. We examine the Nash-equilibrium conditions for single-activity accidents between heterogeneous agents, ‘good’ drivers or ‘bad’ drivers allowing a variable damage function and a liability rule defined on the cube. The relative desirability for society of alternative equilibria and the conditions under which they can obtain are discussed. The constraints which circumscribe the ability of the government to induce an equilibrium involving careful driving are demonstrated. It transpires that when the proportion of good drivers increases, it becomes more difficult to sustain a careful equilibrium whereas an equilibrium of reckless behavior becomes easier to sustain. Various extensions of the models are also presented.     

双边投资协定与外商直接投资——基于信号模型的博弈分析

在Jan Peter Sasse(2011)分析的基础上,进一步放宽其假设条件,利用不完全信息下的信号传递模型,对双边投资协定(Bilateral Investment Treaty,BIT)的信号效应机制进行分析.研究发现:BIT作为东道国传递给投资者的信号,该信号有效的条件在于BIT遵守成本的差异,投资者因此有了区分不同类型东道国的依据.东道国之间的引资竞争关系,会不断升级BIT的版本与内容,直至投资环境较差东道国的遵守成本高至无法覆盖签订BIT所带来的投资收益,此时高标准BIT的二次信号有效.此外,在模型拓展分析的基础之上,试图解释了“为何当前高标准BIT已成为各国所关注的对象?以及投资环境越自由的东道国所签订的BIT标准为何越高?”等问题,这对于理解BIT影响外商直接投资的信号机制提供了新的视角与思路.     

基于粗糙集的突发事件属性约简方法

针对突发事件不完备信息系统中的原始数据存在大量属性冗余的问题,提出一种基于粗糙集的不完备信息系统属性约简方法,以剔除冗余属性,提高知识清晰度。首先对缺失、冗余、噪声以及连续型数据进行预处理;然后进行属性分类,将属性分为条件属性与决策属性,进而建立决策表;最后根据决策表的特征,结合有序加权平均算子的思想,提出一种基于属性重要度的启发式属性约简算法。文末,通过实例验证了方法的正确性与有效性,并利用该方法实现了火灾数据的属性约简。     

Existence of LSs

Let X be a ‐set and be a partition of X into n groups of size 2 and one group G₀ of size 4. A large‐set‐plus denoted by LS is a partition of all ‐transverse triples of X into block sets of 3‐GDD(2ⁿ4¹)s with group set , and two block sets of 3‐GDD(2ⁿ)s with group set . In this paper, we study the existence problem of LSs and give a nearly complete solution.     

On E(s2)‐optimal and minimax‐optimal supersaturated designs with 20 rows and 76 columns

We derive a previously unknown lower bound of 41 for the frequency of of an E(s²)‐optimal and minimax‐optimal supersaturated design (SSD) with 20 rows and 76 columns. This is accomplished by an exhaustive computer search that uses the combinatorial properties of resolvable 2 − (20, 10, 36) designs and the parallel class intersection pattern method. We also classify all nonisomorphic E(s²)‐optimal 4‐circulant SSDs with 20 rows and .     

The Spectrum of （gv,g, 3, λ）-dDF in Zgv

In this paper, several recursive constructions for directed difference family and perfect directed difference family are presented by means of difference matrix and incomplete difference matrix. Finally the necessary and sufficient conditions for the existence of a （gv, g, 3, λ）-directed difference family in Zgv are established. As a consequence, the necessary and sufficient conditions for the existence of a cyclic directed group divisible design with block size three and type gv are obtained.     

The Dattoli-Srivastava conjectures concerning generating functions involving the harmonic numbers

In a recent paper Dattoli and Srivastava [3], by resorting to umbral calculus, conjectured several generating functions involving harmonic numbers. In this sequel to their work our aim is to rigorously demonstrate the truth of the Dattoli-Srivastava conjectures by making use of simple analytical arguments. In addition, one of these conjectures is stated and proved in more general form.