A GENERALIZED GRADIENT METHOD FOR NONLINEAR CONSTRAINTS AND ITS CONVERGENT PROPERTIES

ＡＧＥＮＥＲＡＬＩＺＥＤＧＲＡＤＩＥＮＴＭＥＴＨＯＤＦＯＲＮＯＮＬＩＮＥＡＲＣＯＮＳＴＲＡＩＮＴＳＡＮＤＩＴＳＣＯＮＶＥＲＧＥＮＴＰＲＯＰＥＲＴＩＥＳＧＡＯＺｉｙｏｕ（ＮｏｒｔｈｅｒｎＪｉａｏｔｏｎｇＵｎｉｖｅｒｓｉｔｙ，Ｂｅｉｊｉｎｇ１０００４４，...     

A LOGARITHMIC BARRIER NEWTON METHOD FOR SEMIDEFINITE PROGRAMMING

1.IntroductionInrecentyears,muchattentionhasbeenfocusedonthesemidefiniteprogramming(SDP)problem.OnereasonisthatSDPhasveryimportantapplicationsinmanyareas,suchascombinationaloptimization,systemandcontroltheory,eigenvalueoptimizationetc.[1'2'3]Anotherreason…     

THE OPTIMALITY CONDITIONS OF D-PSEUDOCONVEX PROGRAMMING WITH OPERATOR CONSTRAINTS

The problem of D-pseudoconvex programming with operator con-straints is discussed in this paper.Some new optimality conditions are presentedand an error made by V.Barbu in [4] is pointed out.     

WU-RITT''''S METHOD FOR NONLINEAR CONTROL SYSTEMS

ＷＵ－ＲＩＴＴ＇ＳＭＥＴＨＯＤＦＯＲＮＯＮＬＩＮＥＡＲＣＯＮＴＲＯＬＳＹＳＴＥＭＳ￥ＬＩＳｈｕｒｏｎｇ（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅ，ＡｃａｄｅｍｉａＳｉｎｉｃａ，Ｂｅｉｊｉｎｇ１０００８０，Ｃｈｉｎａ）Ａｂｓｔｒａｃｔ：Ｔｈｉ...     

NONLINEAR GALERKIN METHOD FOR STEADYNONLINEAR DIFFERENTIAL EQUATIONS

1.IntroductionNonlinearGalerkinmethodsarenumericalschemesforthedissipativeevolutionpartialdifferelltialequationswherethespatialdiscretizationreliesonanonlinearmanifoldinsteadofalinearspaceasintheclassicalGalerkinmethod.Moreprecisely,oneconsidersafinitedim…     

A NEW ALGORITHM FOR PURX O-1 LINEAR PROGRAMS WITH INEQUALITY CONSTRAINTS

ＡＮＥＷＡＬＧＯＲＩＴＨＭＦＯＲＰＵＲＸＯ－１ＬＩＮＥＡＲＰＲＯＧＲＡＭＳＷＩＴＨＩＮＥＱＵＡＬＩＴＹＣＯＮＳＴＲＡＩＮＴＳ￥ＣＨＥＮＪｉａｎｆｅｉ（ＢｉｏｃｈｅｍｉｃａｌＥｎｇｉｎｅｅｒｉｎｇＳｔａｔｅＫｅｙＬａｂｏｒａｔｏｒｙ，Ｂｅｉｊｉｎｇ１０...     

A SECOND ORDER DIFFERENCE SCHEME WITH NONUNIFORM MESHES FOR NONLINEAR PARABOLIC SYSTEM

In this paper, a difference scheme with nonuniform meshes is established for the initial-boundary problem of the nonlinear parabolic system. It is proved that the difference scheme is second order convergent in spacestep and timestep.     

STOCHASTIC PROGRAMMING METHOD FORMULTIPERIOD CONSUMPTION AND INVESTMENT PROBLEMS WITH TRANSACTIONS COSTS

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.     

A HYBRID POLYNOMIAL ALGORITHM FOR LINEAR PROGRAMMING

ＡＨＹＢＲＩＤＰＯＬＹＮＯＭＩＡＬＡＬＧＯＲＩＴＨＭＦＯＲＬＩＮＥＡＲＰＲＯＧＲＡＭＭＩＮＧ￥ＨＵＡＮＧＳａｉｎｇ（ＤｅｐａｒｔｍｅｎｔｏｆＩｎｆｏｒｍａｔｉｏｎａｎｄＳｙｓｔｅｍｓＭａｎａｇｅｍｅｎｔ，ＣｏｌｌｅｇｅｏｆＢｕｓｉｎｅｓｓａｎｄＭａｎ...     

A ROBUST DECOMPOSITION OF LINEAR PROGRAMMING USING A GOAL-PARTITIONING METHOD

The Dantzig/Wolfe linear programming decomposition algorithm has had important economicinterpretations as well as a widespread impact on solving large scale linear programming problem.Inthis paper we consider a similar underlying structure,where however there is only one couplinginequality or equation.With this simplification,we demonstrate how to achieve an equitable partitionof the overall coupling resource to individual subproblem constraints through a simple iterationprocedure which appears to be very efficient.     

A VARIATION OF GOLDFARB'S METHOD FOR LINEARLY CONSTRAINED OPTIMIZATION PROBLEMS AND ITS SUPERLINEAR CONVERGENCE RATE

1.IntroductionRosen'sgradientprojectionmethodisaveryinterestingtechniqueinoptimization(see[1,2]),butitsglobalconvergenceisalong-standingopenproblemintheliterature.Thefirstconvergentversionwasfoundbyp.l.k[3].ButPolak'sversionistoocomplicated.Du[4]alsofoundasimplerconvergentversionbydeletingPolak'sspecialprocedure.CombiningRosen'smethodwithvariablemetricmethods,Goldfarb[sl,MurtaghandSargentl'lobtainedtwoefficientalgorithms.Theconvergenceofsuchalgorithmsisstillanopenproblem.However,severalcon…     

A HYBRID METHOD FOR LINEAR PROGRAMMING

1.IntroductionItiswellknownthatsinceKaxmarkax[1]proposedthefirstinferiorpoilltmethod,manyexpertshavebeeninvolvedtoimproveandcompletethismethod.ThereisalotofprogressinthisareaandmanyinteriorpointmethodsaredevelOPed;theinterestedreaderisreferredtotheexcellentbooksofhoandPllthenpura[2]andNesterovandNemirovskiil3].TheseiDteriorpointmethodscanbeclassifiedroughlyintothreecategories:(i)potentialreduction,(n)affinescaling,and(iii)path-following.Theaffine-scalingmethodisshowntoworkwellinpracticebyta…     

A Strong Subfeasible Directions Algorithm with Superlinear Convergence

ＡＳｔｒｏｎｇＳｕｂｆｅａｓｉｂｌｅＤｉｒｅｃｔｉｏｎｓＡｌｇｏｒｉｔｈｍｗｉｔｈＳｕｐｅｒｌｉｎｅａｒＣｏｎｖｅｒｇｅｎｃｅＪＩＡＮＪｉｎｂａｏ（Ｄｅｐｔ．ｏｆＭａｔｈ．ａｎｄＩｎｆｏｒｍａｔｉｏｎＳｃｉｅｎｃｅ，ＧｕａｎｇｘｉＵｎｉｖｅｒｓｉｔｙ...     

AN SQP METHOD BASED ON SMOOTHING PENALTY FUNCTION FOR NONLINEAR OPTIMIZATION WITH INEQUALITY CONSTRAINT

1 IntroductionIn tabs paper, we consider the following nonlinear optbostion problem:where j: Re - R, g: Re - Re are continuously ~ntiable functinns. SoP method forproblem (1) generates a sequence of points which converges to a K--T point of problem (1)through the following iterate formulaxk 1 = x* adds (2)adhere da is the solution of the following quadratic Prograrxuning problemin which Bh is a sylnlnetric positive deflate lllatris and A* is a stepsise obtained by some lineseaxch to redu…     

STOCHASTIC PR0GRAMMING METHOD FOR MULTIPERIOD CONSUMPTION AND INVESTMENT PROBLEMS WITH TRANSACTIONS COSTS

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.