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 Strong Subfeasible Directions Algorithm with Superlinear Convergence

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

一种新颖的花朵授粉优化算法及收敛性分析

针对现有花朵授粉算法存在易早熟、寻优精度不高、搜索效率低下等问题,研究设计了一种改进的花朵授粉算法。该算法利用逻辑自映射函数对花粉粒进行混沌扰动,使缺乏变异机制的花粉粒集具有较强的自适应能力,有效地防止了算法后期最优解趋同的现象。利用变换算子对搜索空间进行动态收缩,使算法在寻优过程中保持较高的种群多样性,降低算法陷入局部极值的概率,从而提高算法的搜索效率和寻优精度。同时,结合花朵授粉的生物学特征,从机理上描述了改进后算法的具体实现步骤,对算法的收敛性和寻优性能进行了详细的剖析,并采用实数编码的方法分析了算法的收敛性,给出了算法的生物学模型和理论基础。实验结果表明,改进后的算法具有较好的性能。     

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.     

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 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…