Accelerated Primal-Dual Projection Neurodynamic Approach With Time Scaling for Linear and Set Constrained Convex Optimization Problems

The Nesterov accelerated dynamical approach serves as an essential tool for addressing convex optimization problems with accelerated convergence rates.Most previous studies in this field have primarily concentrated on unconstrained smooth con-vex optimization problems.In this paper,on the basis of primal-dual dynamical approach,Nesterov accelerated dynamical approach,projection operator and directional gradient,we present two accelerated primal-dual projection neurodynamic approaches with time scaling to address convex optimization problems with smooth and nonsmooth objective functions subject to linear and set constraints,which consist of a second-order ODE(ordinary differential equation)or differential conclusion system for the primal variables and a first-order ODE for the dual vari-ables.By satisfying specific conditions for time scaling,we demonstrate that the proposed approaches have a faster conver-gence rate.This only requires assuming convexity of the objective function.We validate the effectiveness of our proposed two accel-erated primal-dual projection neurodynamic approaches through numerical experiments.

Vertical derivative conversion of irregular-range potential fi eld data based on improved projection onto convex sets method

Gravity and magnetic exploration areas are usually irregular,and there is some data defi ciency.Missing data must be interpolated before the vertical derivative conversion in the wavenumber domain.Meanwhile,for improved processing precision,the data need to be edge-padded to the length required by the fast Fourier transform algorithm.For conventional vertical derivative conversion of potential fi eld data(PFD),only vertical derivative conversion is considered,or interpolation,border padding,and vertical derivative conversion are executed independently.In this paper,these three steps are considered uniformly,and a vertical derivative conversion method for irregular-range PFD based on an improved projection onto convex sets method is proposed.The cutoff wavenumber of the filter used in the proposed method is determined by fractal model fi tting of the radial average power spectrum(RAPS)of the potential fi eld.Theoretical gravity models and real aeromagnetic data show the following:(1)The fitting of the RAPS with a fractal model can separate useful signals and noise reasonably.(2)The proposed iterative method has a clear physical sense,and its interpolation,border padding error,and running time are much smaller than those of the conventional kriging and minimum curvature methods.

Optimal Separation of Twin Convex Sets under Externalities

This paper studies the outcomes of independent and interdependent pair-wise contests between economic agents subject to an optimal external decision problem for each pair. The external decision maker like the government or regulator is faced with the problem of how to devise rules and regulations regarding contests. In this paper, a decision problem is faced under negative and positive externalities. A pair of entities is represented by disjoint convex sets in a small area in a neighborhood. I assume that each entity imposes an equal externality on the other (and the other only) and thus they can be considered to be twins. Among the group of twins in any neighborhood, there is a set of twin pairs such that, for each pair in the set, each twin can impose a strictly negative externality on the other (and the other only), and this is a potential welfare loss which concerns the decision maker. A separating hyper-plane can block the negative externalities between any pair of twins given convexity. However, this can be costly if positive externality from the neighborhood is also blocked by the separation technology. Thus, this paper compares the pair-wise utility from separation to that of non-separation. A simple representation of the decision problem is developed with respect to a single and isolated neighborhood. A complete characterization of the decision problem is obtained with a large number of pair-wise intersecting neighborhoods.

Some Results on the Upper Convex Densities of the Self-Similar Sets at the Contracting-Similarity Fixed Points

In this paper, some results on the upper convex densities of self-similar sets at the contracting-similarity fixed points are discussed. Firstly, a characterization of the upper convex densities of self-similar sets at the contracting-similarity fixed points is given. Next, under the strong separation open set condition, the existence of the best shape for the upper convex densities of self-similar sets at the contracting-similarity fixed points is proven. As consequences, an open problem and a conjecture, which were posed by Zhou and Xu, are answered.

SOME PROPERTIES OF BOUNDED SETS IN INDUCTIVE LIMITS

Let (E,ξ）=indlim (En,ξn） be an inductive limit of a sequence of locally convex spaces,For brevity,denote by (DS) each set Bbounded in (E,ξ） is contained in some En； and (DST) each set B bounded in (E,ξ） is contained and bounded in some (En,ξn）. Theovem 1.(DS) holds provided that (i) for each n∈N,there is a neighborhood Un of o in (En,ξn） and m(n)∈ such that -↑Un^E包含于Em(n),and (ii) for any neighborhood V n of o in (En,ξn）,∞↑Un=1 Vn absorbs every bounded set in (E,ξ）. theorem 2 Let all (En,ξn） be metrizable and (DS) hold,then for each bounded set B IN (E,ξ）and each n ∈N thcrc is a neighborhood U k of o in (Ek,ξk）, 1≤k≤n ,and m(n)∈N such that ——↑(B+U1+U2+…+Un)^E包含于 Em(n). theorem 3. Let all (En,ξn） be Frechet spaces.Then (DST) holds if and only if (i) for each n ∈N,there is u neighborhood U n of in (En,ξn） and m(n)∈N such that 0↑Un^E包含于Em(n),and (ii) for each each closed ,absosed,absolutely conuex,bounded set B in (E,ξ）,∞↑Un=1(（εnB)∩Un）absorbs B,where U n is any neighborhood of o in (En,ξn） and εn is any positive number for every n ∈N。

Structural eigenvalue analysis under the constraint of a fuzzy convex set model

In small-sample problems, determining and controlling the errors of ordinary rigid convex set models are difficult. Therefore, a new uncertainty model called the fuzzy convex set（FCS） model is built and investigated in detail. An approach was developed to analyze the fuzzy properties of the structural eigenvalues with FCS constraints. Through this method, the approximate possibility distribution of the structural eigenvalue can be obtained. Furthermore, based on the symmetric F-programming theory, the conditional maximum and minimum values for the structural eigenvalue are presented, which can serve as nonfuzzy quantitative indicators for fuzzy problems. A practical application is provided to demonstrate the practicability and effectiveness of the proposed methods.

K - Bounded Sets and A - Spaces

Let E and F be two vector spaces in duality with respect to the bilinear pairing 〈,〉. The weak (Mackey,strong) topology on E will be denoted by σ(E,F) (τ(E,F),β(E,F)). In this paper,we show that AE is σ(E,F) K bounded subset if and only if A is β(E,F) K bounded subset. If τ(E′,E) is a quasi barrelled space,we also give a few characterizations for (E,T) to be A space.

Homotopy Method for Non-convex Programming in Unbonded Set

In the past few years, much and much attention has been paid to the method for solving non-convex programming. Many convergence results are obtained for bounded sets. In this paper, we get global convergence results for non-convex programming in unbounded sets under suitable conditions.

Calculus of Generalized Quasi-differentiable Functions I: Some Results on the Space of Pairs of Convex-Set Collections

A Riesz space K1 whose elements are pairs of convex-set collections is presented for the study on the calculus of generalized quasi-differentiable functions. The space K1 is constructed by introducing a well-defined equivalence relation among pairs of collections of convex sets. Some important properties on the norm and operations in K1 are given.

The Ellipsoidal Invariant Set of Fractional Order Systems Subject to Actuator Saturation:The Convex Combination Form

The domain of attraction of a class of fractional order systems subject to saturating actuators is investigated in this paper. We show the domain of attraction is the convex hull of a set of ellipsoids. In this paper, the Lyapunov direct approach and fractional order inequality are applied to estimating the domain of attraction for fractional order systems subject to actuator saturation. We demonstrate that the convex hull of ellipsoids can be made invariant for saturating actuators if each ellipsoid with a bounded control of the saturating actuators is invariant. The estimation on the contractively invariant ellipsoid and construction of the continuous feedback law are derived in terms of linear matrix inequalities (LMIs). Two numerical examples illustrate the effectiveness of the developed method. © 2014 Chinese Association of Automation.

On Starshaped Intuitionistic Fuzzy Sets

Intuitionistic fuzzy starshaped sets (i.f.s.) is a generalized model of fuzzy starshaped set. By the definition of i.f.s., the intuitionistic fuzzy general starshaped sets (i.f.g.s.), intuitionistic fuzzy quasi-starshaped sets (i.f.q-s.) and intuitionistic fuzzy pseudo-starshaped sets (i.f.p-s.) are proposed and the relationships among them are studied. The equivalent discrimination conditions of i.f.q-s. and i.f.p-s. are presented on the basis of their properties which are meaningful for the research of the generalized fuzzy starshaped sets. Moreover, the invariance of the two given fuzzy sets under the translation transformation and linear reversible transformation are discussed.

Convex Set Theory for Reliability Assessment of Steel Beam with Bounded Uncertainty

Probabilistic reliability model established by insufficient data is inaccessible. The convex model was applied to model the uncertainties of variables. A new non-probabilistic reliability model was proposed based on the robustness of system to uncertainty. The non-probabilistic reliability model,the infinite norm model,and the probabilistic model were used to assess the reliability of a steel beam,respectively. The results show that the resistance is allowed to couple with the action effect in the non-probabilistic reliability model. Additionally,the non-probabilistic reliability model becomes the same accurate as probabilistic model with the increase of the bounded uncertain information. The model is decided by the available data and information.

ELEMENTARY DENSITY BOUNDS FOR SELF-SIMILAR SETS AND APPLICATION

Falconer[1] used the relationship between upper convex density and upper spherical density to obtain elementary density bounds for s-sets at H S-almost all points of the sets. In this paper, following Falconer[1], we first provide a basic method to estimate the lower bounds of these two classes of set densities for the self-similar s-sets satisfying the open set condition （OSC）, and then obtain elementary density bounds for such fractals at all of their points. In addition, we apply the main results to the famous classical fractals and get some new density bounds.

Martingales and Super-Martingales Relative to a Convex Set of Equivalent Measures

In the paper, the martingales and super-martingales relative to a convex set of equivalent measures are systematically studied. The notion of local regular super-martingale relative to a convex set of equivalent measures is introduced and the necessary and sufficient conditions of the local regularity of it in the discrete case are founded. The description of all local regular super-martingales relative to a convex set of equivalent measures is presented. The notion of the complete set of equivalent measures is introduced. We prove that every bounded in some sense super-martingale relative to the complete set of equivalent measures is local regular. A new definition of the fair price of contingent claim in an incomplete market is given and the formula for the fair price of Standard Option of European type is found. The proved Theorems are the generalization of the famous Doob decomposition for super-martingale onto the case of super-martingales relative to a convex set of equivalent measures.

Keystroke Dynamics Based Authentication Using Information Sets

This paper presents keystroke dynamics based authentication system using the information set concept. Two types of membership functions (MFs) are computed: one based on the timing features of all the samples and another based on the timing features of a single sample. These MFs lead to two types of information components (spatial and temporal) which are concatenated and modified to produce different feature types. Two Component Information Set (TCIS) is proposed for keystroke dynamics based user authentication. The keystroke features are converted into TCIS features which are then classified by SVM, Random Forest and proposed Convex Entropy Based Hanman Classifier. The TCIS features are capable of representing the spatial and temporal uncertainties. The performance of the proposed features is tested on CMU benchmark dataset in terms of error rates (FAR, FRR, EER) and accuracy of the features. In addition, the proposed features are also tested on Android Touch screen based Mobile Keystroke Dataset. The TCIS features improve the performance and give lower error rates and better accuracy than that of the existing features in literature.

脱萼剂对“浙梨6号”果实品质与着果率的影响

针对“浙梨6号”因部分萼片宿存或残存、果顶尖凸等而影响果实品相问题,选择PBO、氟硅唑、丙环唑3种脱萼剂,以清水为对照进行试验。结果表明:与对照相比,3种脱萼剂处理果实的脱萼率提高23.27~26.01百分点,果顶尖凸率降低24.55~26.44百分点,扁圆果占比、单果质量、可溶性固形物含量分别增加33.19~37.66百分点、37.9~57.1 g和0.68~0.94百分点,但果实偏斜度、全锈果率分别偏高0.54~0.74和18.36~19.23百分点,端正果率、着果率分别下降15.89~21.07和5.43~6.62百分点,差异达显著或极显著水平。上述3种脱萼剂分别选择4000、333.3、444.4 mg·L^(-1)和花序分离期进行喷施,在保证脱萼防凸效果的同时,可有效降低对着果率及果形端正度等的不利影响。

一种结构不确定分析的改进多维平行六面体模型

多维平行六面体模型是一种能够同时考虑相关变量和独立变量的非概率凸集模型,更适用于工程结构中常见的多源不确定性问题。为更加有效合理地度量结构不确定性,提出一种改进多维平行六面体模型。通过定义区间变量的相关角和边缘区间,给出模型不确定域的显式表达式,进而给出依据实验样本点构建多维平行六面体模型的方法。3个算例分析结果表明,改进多维平行六面体模型能够较好地反映区间变量之间的相关性,是一种比传统多维平行六面体模型更为紧凑合理的模型。

二层多目标随机规划逼近弱有效解集的上半收敛性

为研究二层多目标随机规划逼近问题的弱有效解与精确的弱有效解之间的逼近收敛性,针对上、下层都带有约束条件的一类多目标二层随机规划的逼近问题,构建了二层多目标随机规划逼近问题的弱有效解集的上半收敛性理论框架。即在假设下层反馈到上层的最优解集函数为凸函数的前提下,借助严格凸函数的性质,利用多目标随机规划的弱有效解可以表示成相应的单目标随机规划最优解集交集的结构特征,建立了二层多目标随机规划逼近弱有效解集的上半收敛性,提供了逼近方法求解二层多目标随机规划弱有效解集可以近似替代精确的弱有效解集的理论依据。

基于虚拟样本伪标签生成的高光谱图像分类

半监督高光谱图像分类的精度一般随着标记像素数的增加而提高.然而,标签样本的获得费时费力,且依赖于专家知识.针对这个问题,提出了一种通过少量标签样本生成具有伪标签的虚拟样本新方法.基于数学中的凸集理论,所提出的方法利用少量的训练样本可以生成任意多的带有伪标签的虚拟样本,有效地扩大了训练样本集,明显改善了半监督分类器的分类结果.为了验证所提方法的有效性,在Indian Pines和Pavia University两个常用的实际高光谱数据集上进行了广泛测试.实验结果表明,利用所提出的方法在分类具有少量标签样本的高光谱图像时,3个评价分类结果的指标值均有明显提升.

一种连续型不确定性复杂系统博弈理论及算法研究

当前对于不确定性复杂系统博弈的研究,通常情况下有关策略集是离散的,而非连续和随机的。而在复杂经济社会系统中,常常会遇到连续性随机博弈问题,以及系统中数据的确权问题。在此背景下,提出了一种随机博弈的概念,给出连续策略集下N人非合作随机博弈模型均衡解存在性定理,以及复杂信息系统随机博弈模型的构建及其纳什均衡解算法。给出连续策略下不确定性N人非合作随机博弈概念,建立以局中人的最大收益为目标函数的N人非合作随机博弈模型,提出了均衡解的存在性定理;构建了Wasserstein模糊集,之后融合分布鲁棒优化方法以及投资组合优化方法将该模型转化为有限凸规划,并运用遗传算法求解局中人的近似混合策略,最后构建了基于回归分析的纳什均衡求解算法并将纳什均衡解归一化进行确权。实证分析表明,所构建的理论与算法是有效可行的。