A Superlinearly Convergent Directly Strongly Subfeasible Directions Method for Nonlinear Inequality Constrained Optimization A Generalized Projection Variable Metric Method

ＡＳｕｐｅｒｌｉｎｅａｒｌｙＣｏｎｖｅｒｇｅｎｔＤｉｒｅｃｔｌｙＳｔｒｏｎｇｌｙＳｕｂｆｅａｓｉｂｌｅＤｉｒｅｃｔｉｏｎｓＭｅｔｈｏｄｆｏｒＮｏｎｌｉｎｅａｒＩｎｅｑｕａｌｉｔｙＣｏｎｓｔｒａｉｎｅｄＯｐｔｉｍｉｚａｔｉｏｎＡＧｅｎｅｒａｌｉｚｅｄＰ...     

Primal-Dual ε-Subgradient Method for Distributed Optimization

This paper studies the distributed optimization problem when the objective functions might be nondifferentiable and subject to heterogeneous set constraints. Unlike existing subgradient methods, the authors focus on the case when the exact subgradients of the local objective functions can not be accessed by the agents. To solve this problem, the authors propose a projected primaldual dynamics using only the objective function’s approximate subgradients. The authors first prove that the formulate...     

A Superlinearly Convergent Combined PhaseⅠ-PhaseⅡ Subfeasible Method

ＡＳｕｐｅｒｌｉｎｅａｒｌｙＣｏｎｖｅｒｇｅｎｔＣｏｍｂｉｎｅｄＰｈａｓｅⅠ－ＰｈａｓｅⅡＳｕｂｆｅａｓｉｂｌｅＭｅｔｈｏｄＪＩＡＮＪｉｎｂａｏ（ＭａｔｈｅｍａｔｉｃｓａｎｄＩｎｆｏｒｍａｔｉｏｎＳｃｉｅｎｃｅＤｅｐａｒｔｍｅｎｔｏｆＧｕａｎｇｘｉＵ...     

A Multi-Criteria Optimization Method for Electrical Distribution System and Its Analysing in Practice

In this paper,the author explains the problem that we have to consider multiple goalsand multiple factors which are usually affected by others at the same time in practical work forelectrical power distribution system programming.A new mathematics model is set up here formultiple goals programming of electrical power distribution system which includes various load controlalternatives.An arithmetic and current software for the multi-criteria optimization of electrical power     

A New Algorithm for Unconstrained Min-Max Optimization

We have structured the new differential approximation,V_α-approximation,about themaximum function max{f_i(x)}.On the basis of which the kind of minimax algorithms and itsconvergence are proved.Some numerical examples are tested.The results show that the algorithmis better than Madsen's algorithm when the problem is singular     

A Class of Optimization Method for Bilevel Multi-objective Decision Making Problem with the Help of Satisfactoriness

1　 IntroductionWe discuss the following bilevel multi-objective decision making problemmaxx F( x,y) ( 1 a)s.t. G( x,y)≤ 0 ( 1 b)maxyifi( x,yi) ,　 i =1 ,… ,p ( 1 c)s.t. gi( x,gi)≤ 0 ,　 i =1 ,… ,p ( 1 d)where F( x,y) =( F1 ( x,y) ,… ,FM( x,y) ) ,M≥ 2 .x=( x1 ,x2 ,… ,x N) Tand yi=( yi1 ,… ,yin) Tstand for the decision variable of the upper-level decision maker and the decision variable ofthe lower-level i-th decision making unit;y=( y T1 ,… ,y Tp) T;letn =∑pi=1ni;F∶ Rn N → RM…     

A Projection Method for Multiindices Decision Making

1.INTRODUCTIONThecomprehensiveevaluationofeconomicbenefitisoftenencounteredineconomicresearch.Itisactuallyaproblemofmultiindicesdecisionmaking,alsolay'becalledmultiattribute,multicriteria,ormultiobjectivedecisionmakingproblems.Muchresearchonsuchproblemhasbeencarriedout,butitisstillveryimp4tanttodeveloptilenewmethod.On'tilebasisofvectorprojectinn,thispaperfurtherproposesanewprojectiondecisiolllakinglllethod,whichwaseverusedsuccessfullyinthecomprehensiveed-aluationofeconomicbellefitandled…     

A New Method for Recognizing Point Targets

ＡＮｅｗＭｅｔｈｏｄｆｏｒＲｅｃｏｇｎｉｚｉｎｇＰｏｉｎｔＴａｒｇｅｔｓＬｉＨｏｎｇ，ＳｕｎＺｈｏｎｇｋａｎｇ＆ＸｕＨｕｉＩｎｓｔｉｔｕｔｅｏｆＥｌｅｃｔｒｏｎｉｃＥｎｇｉｎｅｅｒｉｎｇ，ＮａｔｉｏｎａｌＵｎｉｖｅｒｓｉｔｙｏｆＤｅｆｅｎｓｅＴｅｃｈ...     

A Method for Hierarchical Subband HDTV Splitting

ＡＭｅｔｈｏｄｆｏｒＨｉｅｒａｒｃｈｉｃａｌＳｕｂｂａｎｄＨＤＴＶＳｐｌｉｔｔｉｎｇ￥ＦｅｎｇＦａｎ（ＵｎｉｖｅｒｓｉｔｙｏｆＥｌｅｃｔｒｏｎｉｃＳｃｉｅｎｃｅａｎｄＴｅｃｈｎｏｌｏｇｙｏｆＣｈｉｎａ，Ｃｈｅｎｇｄｕ６１００５４，Ｃｈｉｎａ）Ｗａｎｇ...     

A New Method for Grey Forecasting Model Group

1 .ＩＮＴＲＯＤＵＣＴＩＯＮＧｒｅｙｓｙｓｔｅｍｔｈｅｏｒｙｗａｓｉｎｉｔｉａｔｅｄｉｎ 1982 [1] .Ｔｈｅｓｙｓｔｅｍｔｈａｔｌａｃｋｓｉｎｆｏｒｍａｔｉｏｎ ,ｓｕｃｈａｓｓｔｒｕｃｔｕｒｅｍｅｓｓａｇｅｓ ,ｏｐｅｒａｔｉｏｎｍｅｃｈａｎｉｓｍｓａｎｄｂｅｈａｖｉｏｒｄｏｃｕｍｅｎｔｓ ,ｉｓｒｅｆｅｒｒｅｄｔｏｇｒｅｙｓｙｓｔｅｍ .Ｆｏｒｅｘａｍｐｌｅ ,ｔｈｅｈｕｍａｎｂｏｄｙ ,ａ ｇｒｉｃｕｌｔｕｒｅ ,ｅｃｏｎｏｍｙ ,ｅｔｃ .,ａｒｅｇｒｅｙｓｙｓｔｅｍｓ .Ｇｒｅｙｆｏｒｅｃａｓｔｉｎｇｉｓｏｎｅ…     

约束变尺度类算法（Ⅱ）——两步超线性收敛的广义投影梯度约束变尺度方向类

将Ｈａｎ－Ｐｏｗｅｌ和文献［１］中算法的思想有机的结合在一起,构造了广义投影梯度约束变尺度方向所满足的线性系统．从而建立了具有两步超线性收敛的广义投影梯度约束变尺度类算法Ｃ．该算法为统一算法模型Ａ提供了一个重要的子类．到此,统一算法模型Ａ已包括了Ｈａｎ－Ｐｏｗｅｌ算法和既约梯度、投影梯度型、广义投影梯度型约束变尺度类算法．从而形成了一个丰富的理论算法库．与此同时,这些算法也被自然的推广到非单调一维搜索的情形．     

A Strong Subfeasible Directions Algorithm with Superlinear Convergence

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

AN ADAPTIVE TRUST REGION METHOD FOR EQUALITY CONSTRAINED OPTIMIZATION

In this paper, a trust region method for equality constrained optlmization based on nondiferentiable exact penalty is proposed. In this algorithin, the trail step is characterized by computation of its normal component being separated from computation of its tangential component, i.e., only the tangential component of the trail step is constrained by trust radius while the normal component and trail step itself have no constraints. The other main characteristic of the algorithm is the decision of trust region radius. Here, the decision of trust region radius uses the information of the gradient of objective function and reduced Hessian. However, Maratos effect will occur when we use the nondifferentiable exact penalty function as the merit function. In order to obtain the superlinear convergence of the algorithm, we use the twice order correction technique. Because of the speciality of the adaptive trust region method, we use twice order correction when p= 0 (the definition is as in Section 2) and this is different from the traditional trust region methods for equality constrained opthnization. So the computation of the algorithm in this paper is reduced. What is more, we can prove that the algorithm is globally and superlinearly convergent.     

基于对角隐式Runge-Kutta公式的无约束优化方法

通过把一个无约束优化问题转化为一个等价的常微分方程,利用二阶半对角隐式Runge Kutta公式构造了求解无约束优化问题的LRKOPT算法。LRKOPT算法具有与IMPBOT方法相似的数值特性,但LRKOPT算法可以看成是最速下降方向与牛顿法方向的非线性组合,而IMPBOT方法为它们两者之间的线性组合。在目标函数为一致凸函数的假设条件下,证明了LRKOPT方法的具有全局收敛和局部超线性收敛性。数值结果表明LRKOPT方法具有很好的数值稳定性并且LRKOPT方法的计算效率优于IMPBOT方法。     

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…     

A TRUST REGION ALGORITHM WITH NULL SPACE TECHNIQUE FOR EQUALITY CONSTRAINED OPTIMIZATION

This paper presents a trust region algorithm with null space technique fornonlinear equality constrained optimization. Considering in the null space methods that,the convergent rate of range space step is faster than the null space step for the most cases,the proposed algorithm computes null steps more often than range space step. Moreover,the new algorithm is based on the reduced Hessian SQP method. Global convergence ofthe proposed algorithm is proved. The effectiveness of the method is demonstrated bysome numerical examples.     

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 ROBUST SQP METHOD BASED ON A SMOOTHING APPROXIMATE PENALTY FUNCTION FOR INEQUALITY CONSTRAINED OPTIMIZATION

1 IntroductionConsider the following inequality constrained optiInization problem:Inin f(x)xeRn(1)s.t. g(x) 5 0where f: R1'-R, g: R"-Rm are cofltinuousIy differentiable functions.SQP method for soIving problem(1) is to gellerate a sequence {xk} converging…     

GLOBAL CONVERGENCE PROPERTIES OF THREE-TERM CONJUGATE GRADIENT METHOD WITH NEW-TYPE LINE SEARCH

In this paper, a new Wolfe-type line search and a new Armijo-type line search are proposed, and some global convergence properties of a three-term conjugate gradient method with the two line searches are proved.