Optimality Conditions for Vector Optimization of Set-valued Maps

Kuhn Tucker optimality conditions and Lagrange multipliers for vector optimization problems with subconvexlike set valued maps wereestablished by Li zemin. Firstly, the concept of generalized subconvexlikeness for set valued maps is introduced in this paper. Then, a theorem of the alternative for generalized subconvexlike set valued maps in real linear spaces is established. Finally, the optimality conditions for vector optimization problems with set valued maps with equality and inequality constraints are obtained with it.     

The Optimality Conditions for Cone-Preinvex Set-Valued Functions

This paper deals with the minimization problems of cone preinvex set valued functions in the topological vector space .The optimality conditions for vector optimization of cone preinvex set valued functions are obtained.     

Optimality Conditions and Lagrange Duality for a Class of Vector Extremum Problems

A sufficient and necessary optimality conditions is established for vector extremum problems with set constraint by applying the alternative theorem under generalized subconvexlike maps in orderd locally-convex Hausdorff spaces. Then, several optimality conditions are obtained for differentiable vector extremum problems with set constraint by applying the sufficient and necessary optimality conditions and the properties of the twice G-differentiable functions. And finally, the vector-valued Lagrange duality is obtained for the vector extremum problems.     

A NEW APPROACH OF OPTIMIZATION

In this paper, a necessary optimality condition of problems with equality constraints is investigated by the implicit function theorem in n-dimensional Euclidean space. A new approach solving these problems is obtained. The number of dimensions of corresponding system of equations is less than the classic Lagrangian multiplier method.     

Optimality Conditions for Nonsmooth Extremum Problems in Topological Vector Spaces

Some new concepts of coneD_s convexity,coneD-s quasiconvexity,cone D-s pseudoconvexity,s right derivative of vector value mapping are proposed;and their related properties are discussed;the optimality necessary conditions and sufficient conditions for constrained extremum problem(VP)involving in cone D-s convex mapping are extablished;the relation between local optimal solution and global optimal solution;as well as the relation between weakly efficient solution and efficient solution for (VP) are derived;the corresponding results generalize the related results of classic convex programming.     

Dual Theory of Nonsmcoth Multiobjective Programming with Set Functions

In this paper,for a nonsmooth multiobjective programming with set functions,Wolfe type duality and MondWeir type duality are established. Weak dual theorem,direct dual the-orem and in verse dual theorem about effictent solution are discussed.     

基于支持向量机非线性筛选水稻苗期抗旱性指标

作物抗旱性指标筛选具小样本、多指标和非线性等特点,传统的基于经验风险最小原则经线性筛选获得的综合指标及在此基础上建立的线性回归模型的合理性受到质疑;基于结构风险最小原则的支持向量机具适于小样本、非线性、泛化推广能力优异等诸多优点,但可解释性差。本文以15个水稻品种苗期反复干旱存活率为因变量,从24个形态生理指标中经支持向量回归(SVR)非线性筛选得苗高、脯氨酸、丙二醛、叶龄、心叶下倒一叶面积、抗坏血酸等6个综合指标,以此建立的SVR模型拟合精度与留一法预测精度均明显优于参比线性模型;如考虑指标测量的简易性,仅以地上部干重、心叶下倒二叶面积、根冠比、叶龄、叶鲜重、心叶下倒一叶面积等6个形态指标进行评估同样可行。为增强SVR的解释能力,基于F测验对SVR模型建立了非线性回归显著性与单因子重要性显著性的测验方法。     

NECESSARY CONDITIONS OF SOLUTIONS FOR VECTOR EXTREMAL PROBLEMS

In this paper, we give the theorems of the alternative, the lag-range multipler theorem, Kuhn-Tucker conditions, saddle poin t optimality conditions and duality theorem concerning efficient and weak efficient solutions when objective function be D-ordered subconvexlike. The results here have extended many conclutions of [1][3][4]     

The Convergence of a 2-Block AOR Method for Large-Scaled Least-Square Problems

A necessary and sufficient condition and some sufficient conditions concerning the convergence of a 2-block AOR method for large-scaled least-square problems are given. It is shown that, by appropriately selecting parameters, the 2-block AOR method is always convergent and the theorem in [3] is only a corollary of this paper.     

THE CLASSIFICATION THEOREM OF THE STATES FOR AN IRREDUCIBLE APERIODIC MARKOV.CHAIN AND ITS APPLICATION ON CERTAIN QUEUEING PROCESS

A sufficient condition of the recurrence and a sufficient and ne- cessary condition of the transience for an irreducible and aperiodic Markvo chain are given in this paper. The theorem 4 and- theorem 5 proved by F, G. Foster [1] are just the particular cases of them. Finally, these results are applied to the embedded Markov chain associated with queueing process so as to resolve the problem of the state classification for M/G/1 queueing process with bulk service studied by Bailey [2].     

Existence of an Arbitrage about Portfolio in an Unequilibrium Market

This article has discussed the problem of an arbitrage about an portfolio in an unequilimarket and got a determinable theorem about existence of an arbitrage about an portfolio. According to this theorem,an arbitrage about portfolio is not existing if there exists a respect martignal measure.A structural result about existence of arbitrage about an portfolio in a market is gotten. All results represent the existence of an arbitrage about an portfolio is related closely to the type of market.     

Prediction and Analyses of Residual Chlorine Based on Support Vector Regression in Urban Water Distribution System

Support vector regression(SVR) algorithm is an application of structural risk minimization principle in function regression.In this paper,a residual chlorine prediction model based on SVR is established by using the data of manual sampling residual chlorine of water distribution system in a certain city in the north of China.SVR model is compared with the artificial neural network and multivariate linear regression.The result shows that SVR model has better generalization ability for small samples,the predicted average relative error of all monitoring points is 1.80%~8.73%,and can achieve unique and globally optimal solutions.It is practical and can solve the problem for small samples of residual chlorine when the fit precision of model is good but the predicted effect is worse.     

Coupled Fixed Point Theorems for Set-valued Nonexpansive Mappings

In strictly convex Banach spaces, by Set valued mappings being monodromied via the optimal approximation for weakly compact convex set and using contraction mapping sequence to approximate nonexpanding mapping.The author has obtained theorems of coupled fixed point for set valued nonexpansive mappings.     

Fixed Points on Complete Metric Spaces and Normed Linear Spaces

By properties of a real function, fixed points problem on two complete metric spaces are discussed.The result generalizes corresponding result of Fisher.Moreover, this result provides a general convergence rate estimate. Meanwhile, we discuss the existence of fixed point on two normed linear spaces under the condition of weak topology, and we obtain a new fixed point theorem.     

OPTIMALITY CONDITIONS IN GENERALIZED VECTOR OPTIMIZATION

This paper studies the constrained and unconstrained optimization.Their objec-tive functions are set-valued map.By using tangent derivative,an analogue of K-T necessary andsufficient optimality conditions is proved.     

THREE CRITICAL POINTS THEOREM AND ITS APPLICATIONS

In this paper, by use of the pseudo-gradient vector field, the three critical points theorem in [2] is extended to the C1 function in the Ba-nach space, and therefore the three critical, points theorem in [5] is strengthened and the existence of the saddle point of the C2 function is discussed.     

Structure of Closed Sets in Fuzzy Matroid

The authors study the properties and structures of fuzzy closed sets and fuzzy hyperplanes.The relationship between the closed set and it's derived matroid's closed set;The intersection of all hyperplanes in matroids is the smallest closed set and its rank is zero;The intersection of all fuzzy hyperplanes in fuzzy matroids is the smallest closed set and its rank is zero;The characteristics of structures of fuzzy closed sets is showed in using mathematical induction;a necessary and sufficient condition has been found in judging whether a fuzzy set is closed or not.     

MAXIMUM PRINCIPLE AND NONTRIVAL SOLUTION FOR A STATIONARY WAVE EQUATION

The boundary-value problem of a non-linear equation is discussed. A necessary condition for existence of nontrival solution and a maximum priciple are proved.     

柑橘黄龙病病原分化及发生规律研究进展

由韧皮部难培养细菌（Candidatus Liberibacter spp.）引起的柑橘黄龙病是一种毁灭性柑橘病害。主要综述了柑橘黄龙病菌的特性及种内分化新进展,病害的潜育期、时空动态及病害循环等田间发生特点,并从寄主植物、传播介体、生存条件等角度对影响病害流行的因素等进行了分析。     

Algorithm of removing outliers in SVR

The outlier and the measurement that an outlier does not fit the theoretical model in the regression problems are defined. The relationship between the theoretical model and the regression model in the regression problem is analyzed. An approximate theorem is proposed and verified by deleting outlier one by one to construct SVR to approximate the theoretical model. An algorithm of detecting outliers in the SVR problems is constructed based on the approximate theorem. The theoretical analysis of the convergence and effectiveness of the proposed algorithm is given. Then, the step-by-step search algorithm is introduced to improve the outlier removing algorithm to remove outliers in SVR with large-scale samples. The theoretical analysis shows that the improved algorithm is convergent and effective. Finally, the samples produced by two test functions and the samples in UCI data set are used for simulation, and the results show that the proposed algorithm is effective and robust.