On the characterization of Pareto-optimal solutions in bicriterion optimization

For bicriterion optimization involving objective functionsf ₁ andf ₂ defined on a decision spaceX, a condition is presented under which the Pareto-optimal points can be characterized as solutions of the scalar optimization problems: Minimizef ₁(x), subject tof ₂(x),x X, which ranges over a certain interval. Using this condition, it is shown how the Pareto-optimal points can be so characterized in both convex and nonconvex situations.The author gratefully acknowledges Dr. Ivan Singer, Institute of Mathematics, Rumanian Academy of Sciences, Bucharest, Rumania, for pointing out the relevance of Remark 7 in Ref. 7 to the results of this note.     

一种高效的人脸三维点云超分辨率融合方法

三维人脸识别技术是当前研究和应用的热点。提出了一种专门针对人脸的三维点云融合方法,通过人脸检测、人脸姿态校正、点云对准和三视点投影等步骤实现三维点云超分辨率融合。实验结果表明,该方法可提高点云的分辨率,降低噪声的干扰,消除孔洞,能较好地重构人脸表面,能大幅度地降低融合的计算复杂度,提高融合的效率。     

Characteristics of semi-convex frontier optimization

We study semi-convex frontier (SCF) optimization problems where objective functions can be semi-convex and constraint sets can be non-polyhedron, which stem from a growing range of optimization applications such as frontier analysis, multi-objective programming in economics. The new findings of this paper can be summarized as follows: (1) We characterize non-dominated points of a non-polyhedron optimal solution set of a semi-convex frontier program. (2) We obtain optimality conditions of a constant modulus SCF program, of which the objective function is semi-convex with a constant semiconvexity modulus. (3) We obtain a non-smooth Hölder stability of the optimal solutions of a semiconvex frontier program. (4) We use generalized differentiability to establish sensitivity analysis of the optimal value function of a semi-convex frontier program.     

Fixed Point Theorems for (p,q)-Quasi-Contraction Mappings in Cone Metric Spaces

In this work, the authors introduce the concept of $(p,q)$-quasi-contraction mapping in a cone metric space. We prove the existence and uniqueness of a fixed point for a $(p,q)$-quasi-contraction mapping in a complete cone metric space. The results of this paper generalize and unify further fixed point theorems for quasi-contraction, convex contraction mappings and two-sided convex contraction of order $2$.     

On nonlinear perturbations of a periodic fractional Schrödinger equation with critical exponential growth

In this paper we study the existence of solutions for fractional Schrödinger equations of the form where V is a potential bounded and the nonlinear term has the critical exponential growth. We prove the existence of at least one weak solution by combining the mountain‐pass theorem with the Trudinger–Moser inequality and a version of a result due to Lions for critical growth in .     

Entropy-expansiveness of geodesic flows on closed manifolds without conjugate points

In this article, we consider the entropy-expansiveness of geodesic flows on closed Riemannian manifolds without conjugate points. We prove that, if the manifold has no focal points, or if the manifold is bounded asymptote, then the geodesic flow is entropy-expansive. Moreover, for the compact oriented surfaces without conjugate points, we prove that the geodesic flows are entropy-expansive. We also give an estimation of distance between two positively asymptotic geodesics of an uniform visibility manifold.     

基于非参数方法的交通流变点问题分析

考虑到交通流数据的分布形式不确定及其变点数目未知的实际情形,以基于非参数方法的交通流变点问题为研究对象,拟通过基于Kolmogorov-Smirnov(KS)检验和Mann-Whitney U检验的滑动窗口法实现变点存在与否的检验,进一步结合二分法对交通流数据变点数目及其位置进行估计.正态分布模拟仿真显示,两种方法对于均值变点检验和估计效果较好,而对于方差变点检验和估计,Mann-Whitney U方法不及K-S方法.最后,贵阳市中心道路车流量数据实例分析,表明方法对于交通流突变分析效果较好,可为相关部门提供可靠的决策依据.     

基于VE理论的LCC与直觉模糊TOPSIS法的项目成本方案分析

将价值工程运用到全寿命周期成本分析中,计算方案的动态成本.通过解决传统层次分析法难以解决的模糊环境中的综合评价问题,提出直觉模糊层次分析法并求得各方案的功能系数,然后与方案LCC得到价值系数,以此为依据进行方案评选.为了使方案评选结果更加科学合理,利用直觉模糊TOPSIS法进行对比分析与验证.结合某住宅项目,得到两种评价结果的一致性,证明方法对于成本方案的评选是有效的.     

代表点数目对概率密度演化方法分析精度的影响

基于物理随机地震动模型和切球选点法生成3组不同容量地震动样本,以此作为外激励输入,采用概率密度演化方法分别对结构进行随机地震反应分析,并对分析结果进行比较,以研究代表点数目对分析精度的影响.数值分析结果表明,基于切球选点法生成的少量代表样本能够对目标总体的一、二阶统计特性进行较为准确地估计;当样本容量较小时,结构随机动力响应在各时刻的概率分布分析结果具有一定的误差.因此,应根据随机动力系统中随机变量的数目、所采用的选点方法以及预期的计算精度合理确定概率密度演化方法中样本的容量.