New Imperfect Conjugate Gradient Algorithm

We present a method which generates conjugate search directions and maintains the quadratic convergence property, when applied to a quadratic function, even when the line searches are not exact. The method is similar to that given by Dixon, but needs one less vector store. When the method is applied to a number of general functions of different dimensionality, results show the efficiency of the method.     

弱1—凸对策及其解的性质

本文提出了一类特殊的ｎ人合作对策模型─—弱１—凸对策，研究了弱１—凸对策的解的性质，并证明弱１—凸对策的解满足所有常见的公理化特征．     

η-Invariant and Flat Vector Bundles

Abstract We present an alternate definition of the mod Z component of the Atiyah-Patodi-Singer η invariant associated to (not necessary unitary) flat vector bundles, which identifies explicitly its real and imaginary parts. This is done by combining a deformation of flat connections introduced in a previous paper with the analytic continuation procedure appearing in the original article of Atiyah, Patodi and Singer. * Project supported by the Cheung-Kong Scholarship of the Ministry of Education of China and the 973 Project of the Ministry of Science and Technology of China. (Dedicated to the memory of Shiing-Shen Chern)     

The uv-Decomposition on a Class of D.C. Functions and Optimality Conditions

In this paper,the UV-theory and P-differential calculus are employed to study second-order ex-pansion of a class of D.C.functions and minimization problems.Under certain conditions,some properties ofthe U-Lagrangian,the second-order expansion of this class of functions along some trajectories are formulated.Some first and second order optimality conditions for the class of D.C.optimization problems are given.     

物质纯重力场部分的能量-动量张量研究

认为物质的质量(能量)存在形式可分为两部分，一部分是以纯物质形式存在的，另一部分是以纯重力场形式存在的.物质质量(能量)这两种形式各自对应着相应的能量 动量张量，物质总的能量-动量张量可表示为Tμν=T(Ⅰ)μν+T(Ⅱ)μν,这里，T(Ⅰ)μν，T（Ⅱ）μν分别代表物质纯物质部分和纯重力场部分的能量-动量张量.通过类比电磁理论，定义：ωμ≡-c2gμ0/g00,并引入一个反对称张量Dμν=ωμ/xν-ων/xμ，则物质纯重力场部分的能量-动量张量为T(Ⅱ)μν=(DμρDρν-gμνDαβDαβ/4 关键词： 能量-动量张量 纯重力场 重力场方程 标量重力势 矢量重力势     

Optimal Investment in a Levy Market

In this paper we consider the optimal investment problem in a market where the stock price process is modeled by a geometric Levy process (taking into account jumps). Except for the geometric Brownian model and the geometric Poissonian model, the resulting models are incomplete and there are many equivalent martingale measures. However, the model can be completed by the so-called power-jump assets. By doing this we allow investment in these new assets and we can try to maximize the expected utility of these portfolios. As particular cases we obtain the optimal portfolios based in stocks and bonds, showing that the new assets are superfluous for certain martingale measures that depend on the utility function we use.     

The node-edge weighted 2-edge connected subgraph problem: Linear relaxation, facets and separation

Let G=(V,E) be a undirected k-edge connected graph with weights c_e on edges and w_v on nodes. The minimum 2-edge connected subgraph problem, 2ECSP for short, is to find a 2-edge connected subgraph of G, of minimum total weight. The 2ECSP generalizes the well-known Steiner 2-edge connected subgraph problem. In this paper we study the convex hull of the incidence vectors corresponding to feasible solutions of 2ECSP. First, a natural integer programming formulation is given and it is shown that its linear relaxation is not sufficient to describe the polytope associated with 2ECSP even when G is series-parallel. Then, we introduce two families of new valid inequalities and we give sufficient conditions for them to be facet-defining. Later, we concentrate on the separation problem. We find polynomial time algorithms to solve the separation of important subclasses of the introduced inequalities, concluding that the separation of the new inequalities, when G is series-parallel, is polynomially solvable.     

Integration and propagation of a multi-criteria decision making model in constraint programming

In this paper we propose a general integration scheme for a Multi-Criteria Decision Making model of the Multi-Attribute Utility Theory in Constraint Programming. We introduce the Choquet integral as a general aggregation function for multi-criteria optimization problems and define the Choquet global constraint that propagates this function during the Branch-and-Bound search. Finally the benefits of the propagation of the Choquet constraint are evaluated on the examination timetabling problem.     

A Verified Optimization Technique to Locate Chaotic Regions of Hénon Systems

We present a new verified optimization method to find regions for Hénon systems where the conditions of chaotic behaviour hold. The present paper provides a methodology to verify chaos for certain mappings and regions. We discuss first how to check the set theoretical conditions of a respective theorem in a reliable way by computer programs. Then we introduce optimization problems that provide a model to locate chaotic regions. We prove the correctness of the underlying checking algorithms and the optimization model. We have verified an earlier published chaotic region, and we also give new chaotic places located by the new technique.     

A Constraint Programming Approach to Extract the Maximum Number of Non-Overlapping Test Forms

This paper introduces a novel approach for extracting the maximum number of non-overlapping test forms from a large collection of overlapping test sections assembled from a given item bank. The approach involves solving maximum set packing problems (MSPs). A branch-and-bound MSP algorithm is developed along with techniques adapted from constraint programming to estimate lower and upper bounds on the optimal MSP solution. The algorithm is general and can be applied in other applications including combinatorial auctions. The results of computer simulations and experiments with an operational item bank are presented. An erratum to this article is available at .