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GENERALIZED K-T CONDITIONS AND PENALTY FUNCTIONS FOR QUASIDIFFERENTIABLE PROGRAMMING

Applied Mathematics(A Journal of Chinese Universities) 1999年第1期14卷 85-89页

作者： YinHongyou xuchengxian SchoolofScience Xi＇anJiaotongUniv.Xi＇an710049. SchoolofScience Xi＇anJiaotongUniv.Xi＇an710049.

Abstract In this paper,a quasidifferentiable programming problem with inequality constraints is ***,a general form of optimality conditions for this problem is given,which contains the results of Luderer,Kuntz and ***,a new generalized K T condition is *** new optimality condition doesnt use Luderers regularity assumption and its Lagrangian multipliers dont depend on the particular elements in the superdifferentials of the object function and constraint ***,a penalty function for the problem is *** conditions of the penalty function attaining a global minimum are obtained.

关键词： 1991 MR Subject Classification 49K30 90C30

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FILLED FUNCTIONS FOR UNCONSTRAINED GLOBAL OPTIMIZATION

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Applied Mathematics(A Journal of Chinese Universities) 2000年第3期15卷 307-318页

作者： XuZheng xuchengxian FacultyofSciences Xi＇anJiaotongUniv.Xi＇an710049 FacultyofElectricalEngineering Xi＇anJiaotongUniv.Xi＇an710049

The paper is concerned with the filled functions for global optimization of a continuous function of several *** general forms of filled functions are presented for smooth and nonsmooth *** functions have either two adjustable parameters or one adjustable *** on functions and on the values of parameters are given so that the constructed functions are desired filled functions.

关键词： Global optimization filled function nonsmooth optimization basin.

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A HYBRID METHOD FOR SOLVING VARIATIONAL INEQUALITY PROBLEMS

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Applied Mathematics(A Journal of Chinese Universities) 2000年第4期15卷 470-482页

作者： LiangXiming LiFei xuchengxian CollegeofInformationScienceandEngineering CentralSouthUniv.Changsha410083. SchoolofScience Xi＇anJiaotongUniv.Xi＇an710049

By using Fukushima's differentiable merit function,Taji,Fukushima and Ibaraki have given a globally convergent modified Newton method for the strongly monotone variational inequality problem and proved their method to be quadratically convergent under certain assumptions in *** this paper a hybrid method for the variational inequality problem under the assumptions that the mapping F is continuously differentiable and its Jacobian matrix Δ F(x) is positive definite for all x∈S rather than strongly monotone and that the set S is nonempty,polyhedral,closed and convex is *** type line search and trust region strategies as well as Fukushima's differentiable merit function are incorporated into the *** is then shown that the method is well defined and globally convergent and that,under the same assumptions as those of Taji et al.,the method reduces to the basic Newton method and hence the rate of convergence is *** experiences show the efficiency of the proposed method.

关键词： Variational inequality problem line search trust region strategy hybrid method global convergence quadratic convergence.

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STOCHASTIC PROGRAMMING METHOD FOR MULTIPERIOD CONSUMPTION AND INVESTMENT PROBLEMS WITH TRANSACTIONS COSTS

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Journal of Systems Science & Complexity 2004年第1期17卷 39-53页

作者： CHENZhiping xuchengxian K.C.Yuen DepartmentofScientificComputingandAppliedSoftwares FacultyofScienceXi'anJiaotongUniversityXi'an710049China DepartmentofStatisticsandActuarialScience TheUniversityofHongKongPokfulamRoadHongKongChina DepartmentofScientificComputingandAppliedSoftwares FacultyofScienceXi'anJiaotongUniversityXi'an710049China

Using the GARCH model to describe the risky asset's return process so thatits time-varying moments and conditional heteroskedasticity can be properly reflected,general multiperiod optimal investment and consumption problems with both fixed andproportional transactions costs are investigated in this paper. We model this kind ofdifficult problems as a dynamic stochastic optimization problem, which can cope withdifferent utility functions and any number of time periods. The procedure to solve theresulting complex nonlinear stochastic optimization problem is discussed in detail and abranch-decomposition algorithm is devised.

关键词： consumption and investment problems the GARCH model stochastic programming decomposition

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