Economic Equilibrium: Optimality and Price Decentralization

Mathematical economics has a long history and covers many interdisciplinary areas between mathematics and economics. At its center lies the theory of market equilibrium. The purpose of this expository article is to introduce mathematicians to price decentralization in general equilibrium theory. In particular, it concentrates on the role of positivity in the theory of convex economic analysis and the role of normal cones in the theory of non-convex economies.     

Differential Conditions for Constrained Nonlinear Programming via Pareto Optimization

We deal with the differential conditions for local optimality. The conditions that we derive for inequality constrained problems do not require constraint qualifications and are the broadest conditions based on only first-order and second-order derivatives. A similar result is proved for equality constrained problems, although the necessary conditions require the regularity of the equality constraints.     

有效点、弱有效点和真有效点的锥刻画

利用集合在某点的相依切锥、法向锥和可行方向锥等研究向量优化问题的有效点、 弱有效点和真有效点的特征,对局部有效点、局部弱有效点和局部真有效点与集合的各 锥之间的关系作了刻画.     

Parallelization of population-based multi-objective meta-heuristics: An empirical study

In single-objective optimization it is possible to find a global optimum, while in the multi-objective case no optimal solution is clearly defined, but several that simultaneously optimize all the objectives. However, the majority of this kind of problems cannot be solved exactly as they have very large and highly complex search spaces. Recently, meta-heuristic approaches have become important tools for solving multi-objective problems encountered in industry as well as in the theoretical field. Most of these meta-heuristics use a population of solutions, and hence the runtime increases when the population size grows. An interesting way to overcome this problem is to apply parallel processing. This paper analyzes the performance of several parallel paradigms in the context of population-based multi-objective meta-heuristics. In particular, we evaluate four alternative parallelizations of the Pareto simulated annealing algorithm, in terms of quality of the solutions, and speedup.     

自伴算子代数上的某些*-自同态的σ-弱混合性

设A是希尔伯特空间H上的自伴算子代数,α是A上的*-自同态.如果存在单位向量e∈H,使得对任意α∈A和单位向量h∈H,有lim_(n→∞)〈α~n(a)h,h〉=〈αe,e〉成立,那么称α是A上的σ-弱混合的*-自同态.本文研究了这一有趣性质,并得到了一个*-自同态是σ-弱混合的充分条件.     

Positive value of information in games

We exhibit a general class of interactive decision situations in which all the agents benefit from more information. This class includes as a special case the classical comparison of statistical experiments à la Blackwell. AMS 2000 Subject Classification:Primary 91A35.The work of Bruno Bassan and Marco Scarsini was partially supported by MIUR-COFIN. The authors express their thanks to Sylvain Sorin for enlightening comments.     

优化路问题的代数方法—论动态规划（Ⅱ）

本文用同一思路求解多阶段有向图中三种优化路问题:最优路、N阶最优路及多指标Pareto优化路问题,它们都服从嘉量原理,都用同一个代数公式表达它们的嘉量,并可在同一种表格中进行计算,只是所在半域不同,以本文的方法讨论动态规划中一些离散决定型典型应用问题,其提法、建模思路以及求解过程都有可观的扩大与改善。     

两类记录值之和的中心极限定理

该文给出了Ｌｏｇｉｓｔｉｃ分布纪录值序列部分和的中心极限定理；对于Ｐａｒｅｔｏ分布纪录值序列的部分和T_n，获得了ｌｎT_n的中心极限定理．这一工作不仅具有概率论的极限理论方面的研究价值，而且在金融、保险等领域也具有相当重要的应用前景．     

拓扑线性空间中的Drop定理和Phelps引理以及Ekeland变分原理

将Phelps引理, Ekeland变分原理, Pareto有效性定理推广到拓扑线性空间,同时证明了这三个定理与郑喜印证明的拓扑线性空间中的Drop定理彼此等价．     

Approximate necessary conditions for locally weak Pareto optimality

Necessary conditions for a given pointx ⁰ to be a locally weak solution to the Pareto minimization problem of a vector-valued functionF=(f ₁,...,f _m ),F:XR ^m,XR ^m, are presented. As noted in Ref. 1, the classical necessary condition-conv {Df ₁(x ⁰)|i=1,...,m}T ^*(X, x ⁰) need not hold when the contingent coneT is used. We have proven, however, that a properly adjusted approximate version of this classical condition always holds. Strangely enough, the approximation form>2 must be weaker than form=2.The authors would like to thank the anonymous referee for the suggestions which led to an improved presentation of the paper.