CONVEXIFICATION AND CONCAVIFICATION METHODS FOR SOME GLOBAL OPTIMIZATION PROBLEMS

In this paper, firstly, we propose several convexification and concavification transformations to convert a strictly monotone function into a convex or concave function, then we propose several convexification and concavification transformations to convert a non-convex and non-concave objective function into a convex or concave function in the programming problems with convex or concave constraint functions, and propose several convexification and concavification transformations to convert a non-monotone objective function into a convex or concave function in some programming problems with strictly monotone constraint functions. Finally, we prove that the original programming problem can be converted into an equivalent concave minimization problem, or reverse convex programming problem or canonical D.C. programming problem. Then the global optimal solution of the original problem can be obtained by solving the converted concave minimization problem, or reverse convex programming problem or canonical D.C     

A Decision Support System for Economic Development and Price Reform

In this paper, we present a real decision support system applied to China's macroeconomic management. The structure, design and functions of the system are discussed, and the problems occurring in designing and making the system are also studied. A case study for China's petroleum price reform is given at the end of the paper.     

FORECASTING NIKKEI 225 INDEX WITH SUPPORT VECTOR MACHINE

Support Vector Machine (SVM) is a very specific type of learning algorithms characterized by the capacity control of the decision function, the use of the kernel functions and the sparsity of the solution. In this paper, we investigate the predictability of financial movement direction with SVM by forecasting the weekly movement direction of NIKKEI 225 index. To evaluate the forecasting ability of SVM, we compare the perfor-mance with those of Linear Discriminant Analysis, Quadratic Discriminant Analysis and Elman Backpropagation Neural Networks. The experiment results show that SVM outperforms other classification methods. Furthermore, we propose a combining model by integrating SVM with other classification methods. The combining model performs the best among the forecasting methods.     

THE RANKINGS OF CONTROL SYSTEMS AND APPLICATIONS

The notion of ranking was initiated into control theory by Glad a few yearsago. In this paper we mainly discuss one kind of rankings and study its invarianceproperties. This kind of rankings is closely related to the structure algorithm. The relationsbetween invariants of this kind of rankings and the invariants given by other studies, e.g.the invertibility indices of a system and so on, are examined. As applications of rankings,we deal with some well-known problems in "ranking technique". In this paper we mainlyintroduce a new method rather than solve new problems.     

EXTENDED CASIMIR APPROACH TO CONTROLLED HAMILTONIAN SYSTEMS

In this paper,we first propose an extended Casimir method for energy-shaping.Then itis used to solve some control problems of Hamiltonian systems.To solve the H_x control problem,theenergy function of a Hamiltonian system is shaped to such a form that could be a candidate solution ofHJI inequality.Next,the energy function is shaped as a candidate of control ISS-Lyapunov function,and then the input-to-state stabilization of port-controlled Hamiltonian systems is achieved.Someeasily verifiable sufficient conditions are presented.     

A Class of Plurisubharmonic Functions of Positively Homogeneous of Order ρ

1　 IntroductionThe surjectivity of convolution operator and in particular of linear partial differrentialoperators with constant coefficients is often equivalent to a problem of division in anappropriate space of entire functions.Those problems often have a tight connection withthe study of plurisubharmonic functions and weight system.In this paper we construct aclass of plusisubharmonic functions of positively homogeneous oforderρ and some weightsystem,and discuss their properties.These res…     

Local prediction of the chaotic fh-code based on LS-SVM

Support vector machine （SVM） is powerful to solve some problems such as nonlinear classification, function estimation and density estimation. To consider the chaotic fh （frequency hopping）-code＇s characters in chaotic dynamic system, the forecasting model of the support vector machine in combination with Takens＇ delay coordinate phase reconstruction of chaotic times is established and the least squares model for large-scale problems is used in local training for this model. Finally, a fh-code series generated by Logistic-Kent mapping is applied to verify the local prediction model. Simulation results show that the high accuracy and fault tolerant SVM model has an excellent performance in predicting the fh code, with a very low mean square error and a high relative coefficient.     

ON CONSTRUCTING THE NATURAL EXPONENTIAL FAMILIES WITH POLYNOMIAL VARIANCE FUNCTIONS

In this paper,we discuss the regular exponential family(REF),a natural exponentialfamily with minimum dimension and with the mean function m=E_θX taken as a new parameter.Wepoint out the importance of the REF with polynomial variance function(PVF-REF).When m is asingle factor of PVF and the left end of its defined domain is zero,the corresponding REF is givenas the single-side lattice distribution family;other PVF-REFs can be obtained by a limit process.As an illustration,the results for all seven cases of polynomial variance functions of third degreeare given.     

Parameter selection of support vector machine for function approximation based on chaos optimization

The support vector machine （SVM） is a novel machine learning method, which has the ability to approximate nonlinear functions with arbitrary accuracy. Setting parameters well is very crucial for SVM learning results and generalization ability, and now there is no systematic, general method for parameter selection. In this article, the SVM parameter selection for function approximation is regarded as a compound optimization problem and a mutative scale chaos optimization algorithm is employed to search for optimal paraxneter values. The chaos optimization algorithm is an effective way for global optimal and the mutative scale chaos algorithm could improve the search efficiency and accuracy. Several simulation examples show the sensitivity of the SVM parameters and demonstrate the superiority of this proposed method for nonlinear function approximation.     

Solving the State Equation of a System by Walsh Function

In this paper, We deal with the solution of the state equation of a system by the Walsh function, that is, we shall find the solution of a matrix differential equation by the Walsh function, and introduce a solution of the higher-order matrix differential equation. First, after a certain transform, we turn the higher-order matrix differential equation into a state equation. Then we find the solution of the state equation by the Walsh function. Finally after a certain transform, we obtain a solution of the higher-order matrix differential equation.     

The Refined Solutions on Multiobjective Programming Problems with Fuzzy Parameters in the Constraints

This paper investigates the multiobjective programming problems with fuzzy parameters in the constraints. First, by the decomposing theorem, we introduce a fuzzy set to characterize the constraints, then give the definition of α-quasi-efficient solution and a-efficient solution, and discuss their properties. Finally, a numerical example is presented to illustrate the differences between the refined solutions and the α-Pareto solution.     

Zeroth-Order Methods for Online Distributed Optimization with Strongly Pseudoconvex Cost Functions

This paper studies an online distributed optimization problem over multi-agent systems.In this problem, the goal of agents is to cooperatively minimize the sum of locally dynamic cost functions. Different from most existing works on distributed optimization, here we consider the case where the cost function is strongly pseudoconvex and real gradients of objective functions are not available. To handle this problem, an online zeroth-order stochastic optimization algorithm involving the single-poi...     

Talking About the PHS-ETC Online System

The PHS （Personal Handy phone System） technology developed in Japan realized high quality and low cost mobile communication in a micro cell and abundant valueadded services. Having considered many advantages of PHS, this paper proposed PHS-ETC online system as a technological evolution to substitute for the traditional DSRC-ETC. After comparing DSRC with PHS, this paper discussed the framework and layer structure of the DSRC and PHS system. Besides the functions concerned as vehicle identification and wireless communication, this paper also designed routing identification and toll apportionment functions to meet the needs of ETC. And the newly-designed functions could not be provided by DSRC system. By appending the Presentation Layer, the system could make full use of the existing function modules of DSRC and PHS, and the reconstruction would be greatly saved. Moreover, the system could extend many value-added services of PHS to the expressway, such as real-time traffic advisories, up-to-date navigation guidance, emergency communication, etc.     

MINIMAX INVARIANT ESTIMATOR OF CONTINUOUS DISTRIBUTION FUNCTION UNDER LINEX LOSS

In this paper we consider the problem of estimation of a continuous distribution function under the LINEX loss function. The best invariant estimator is obtained and proved to be minimax for any sample size n ≥ 1.     

On the axioms of revealed preference in fuzzy consumer theory

The revealed preference is a central subject in classical consumer theory.Authors likeSamuelson,Arrow,Richter,Sen,Uzawa and others have proposed an axiomatic setting of revealedpreference theory.Consequently revealed preference axioms WARP and SARP and congruence axioms WCA andSCA have been considered.An important theorem of Sen establishes the equivalence between these axioms provided thefamily of budgets includes all non-empty finite sets of bundles.Fuzzy consumer theory(＝fuzzy choice functions)is a topic that appears in a lot of papers.Particularly,Banerjee studies in fuzzy context axioms of revealed preference and congruenceextending some results of Arrow and Sen.In this paper we modify the Banerjee definition of a fuzzy choice function(＝fuzzy consumer)and we study some fuzzy versions of the axioms of revealed preference and congruence.Banerjeefuzzifies only the range of a consumer;we use a fuzzification of both the domain and the range of aconsumer.The axioms WAFRP,SAFRP,WFCA,SFCA generalize to fu     

An approach to group decision making based on interval fuzzy preference relations

In this paper, we investigate group decision making problems where the decision information given by decision makers takes the form of interval fuzzy preference relations. We first give an index to measure the similarity degree of two interval fuzzy preference relations, and utilize the similarity index to check the consistency degree of group opinion. Furthermore, we use the error-propagation principle to determine the priority vector of the aggregated matrix, and then develop an approach to group decision making based on interval fuzzy preference relations. Finally, we give an example to illustrate the developed approach.     

EMERGENCE FROM LOCAL EVALUATION FUNCTION

This paper presents a new look on emergence from the aspect of locality and globality of evaluation functions for solving traditional computer problems. We first translate the Constraint Satisfaction Problem (CSP) into the multi-agent system, and then show how a global solution emerges from the system in which every agent uses a local evaluation function to decide its action, while comparing to other traditional algorithms,such as Local search and Simulated Annealing which use global evaluation functions. We also give some computer experimental results on large-scale N-queen problems and k-Coloring problems, and show that emergence only depends on problem instance, not details of agent settings, i.e. in some CSPs, the system can self-organize to a global solution~ but can not in some other CSPs no matter what settings of agents have.     

ON CHARACTERIZATIONS OF D-η-PROPERLY PREQUASI-INVEX FUNCTION

Recently, various concepts of D-η-properly prequasi-invex functions were introduced and characterizations of D-η-properly prequasi-invex functions were presented under a certain set of conditions. In this paper, we show that the same results can be obtained under weaker assumptions.     

NOISY OBSERVATION BASED STABILIZATION AND OPTIMIZATION FOR UNKNOWN SYSTEMS

The paper addresses optimization of a performance function which either is optimized via stabilizing and controlling the underlying unknown system or is directly optimized on the basis of its noise-corrupted observations. For the first case the unknown system is identified and then the indirect adaptive control approach is applied to optimize the performance function. For the second case the stochastic approximation method is used to optimize the objective function, and it appears that a number of problems arising from applications may be reduced to the one solvable by this approach. The paper demonstrates some basic results in the area, but with no intention to give a complete survey.     

A FRAMEWORK OF FUZZY LANDSCAOE THEORY WITH AN APPLICATION TO ALLIANCE ANALYSIS

In this paper,we provide a framework of fuzzy landscape theory and discuss an application to alliance analysis.The fuzzy landscape theory may allow us to analyses a variety of aggregation processes in political,economic,and social problems in a more flexible manner.The simulation 3results for the problems of the international alignment of the Second World War in Europe and the coalition formation in standard-setting alliances in the case of the UNIX operation system are compared with those given by the original theory.