共查询到20条相似文献,搜索用时 296 毫秒
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周轩伟 《高校应用数学学报(A辑)》2016,(1):63-72
研究了一类非光滑多目标规划问题.这类多目标规划问题的目标函数为锥凸函数与可微函数之和,其约束条件是Euclidean空间中的锥约束.在满足广义Abadie约束规格下,利用广义Farkas引理和多目标函数标量化,给出了这一类多目标规划问题的锥弱有效解最优性必要条件. 相似文献
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给出了(h,(?)-η伪凸函数的概念,利用Ben-Tal广义代数运算讨论了 它与η-伪凸函数之间的关系.当目标函数和约束函数均为(h,(?))-可微函数时,在广义 Slater约束规格下,得到了相应规划问题取得最优解的Kuhn-Tucker必要条件. 相似文献
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一类非光滑多目标规划的K-T必要条件 总被引:3,自引:1,他引:2
本文对一类由可微函数与凸函数之和形式组成目标函数的多目标规划,分别在Kuhn-Tucker约束品性和Arrow—Hurwicz—Uzawa约束品性下,给出了其弱有效解的K—T必要条件,并给出了其特例(目标函数含||Bx||p的情形)的K—T必要条件,从而推广和改进了已有的结果。 相似文献
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(h,ψ)-数学规划问题的必要条件 总被引:1,自引:0,他引:1
给出了(h,ψ)-η伪凸函数的概念,利用Ben-Tal广义代数运算讨论了它与η-伪凸函数之间的关系。当目标函数和约束函数均为(h,ψ)-可微函数时,在广义Slater约束规格下,得到了相应规划问题取得最优解的Kuhn-Tucker必要条件。 相似文献
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提出了(F,α,ρ,θ)-b-凸函数的概念,它是一类新的广义凸函数,并给出了这类广义凸函数的性质.在此基础上,讨论了目标函数和约束函数均为(F,α,ρ,θ)-b-凸函数的多目标分式规划,利用广义K-T条件,得到了这类多目标规划有效解和弱有效解的几个充分条件,推广了已有文献的相关结果. 相似文献
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本文给出了一类线性约束下不可微量优化问题的可行下降方法,这类问题的目标函数是凸函数和可微函数的合成函数,算法通过解系列二次规划寻找可行下降方向,新的迭代点由不精确线搜索产生,在较弱的条件下,我们证明了算法的全局收敛性 相似文献
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非可微二层凸规划的最优性条件 总被引:3,自引:0,他引:3
本文考虑的是构成函数为非可微凸函数的二层规划问题(NDBP),得到了下层极值函数和上层复合目标函数的方向导数和次微分的估计式,给出非可微二层凸规划(NDBP)最优解的几种最优性条件。 相似文献
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The class of nondifferentiable problems treated in this paper constitutes the dual of a class of convex differentiable problems. The primal problem involves faithfully convex functions of linear mappings of the independent variables in the objective function and in the constraints. The points of the dual problem where the objective function is nondifferentiable are known: the method presented here takes advantage of this fact to propose modifications necessary in the reduced gradient method to guarantee convergence. 相似文献
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Haibin Zhang Juan Wei Meixia Li Jie Zhou Miantao Chao 《Journal of Global Optimization》2014,58(1):169-188
We consider a class of nonsmooth convex optimization problems where the objective function is the composition of a strongly convex differentiable function with a linear mapping, regularized by the group reproducing kernel norm. This class of problems arise naturally from applications in group Lasso, which is a popular technique for variable selection. An effective approach to solve such problems is by the proximal gradient method. In this paper we derive and study theoretically the efficient algorithms for the class of the convex problems, analyze the convergence of the algorithm and its subalgorithm. 相似文献
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本文讨论上层目标函数以下层子系统目标函数的最优值作为反馈的一类二层凸规划的对偶规划问题 ,在构成函数满足凸连续可微等条件的假设下 ,建立了二层凸规划的 Lagrange对偶二层规划 ,并证明了基本对偶定理 . 相似文献
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This paper studies a class of multiobjective generalized fractional programming problems, where the numerators of objective functions are the sum of differentiable function and convex function, while the denominators are the difference of differentiable function and convex function. Under the assumption of Calmness Constraint Qualification the Kuhn-Tucker type necessary conditions for efficient solution are given, and the Kuhn-Tucker type sufficient conditions for efficient solution are presented under the assumptions of (F, α, ρ, d)-V-convexity. Subsequently, the optimality conditions for two kinds of duality models are formulated and duality theorems are proved. 相似文献
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Kazimierz Malanowski 《Mathematical Programming》1985,33(3):352-361
We consider a family of convex programming problems that depend on a vector parameter, characterizing those values of parameters at which solutions and associated Lagrange multipliers are Gâteaux differentiable.These results are specialized to the problem of the metric projection onto a convex set. At those points where the projection mapping is not differentiable the form of Clarke's generalized derivative of this mapping is derived. 相似文献
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R. Kasimbeyli 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(7):2534-2547
In this paper we study optimality conditions for optimization problems described by a special class of directionally differentiable functions. The well-known necessary and sufficient optimality condition of nonsmooth convex optimization, given in the form of variational inequality, is generalized to the nonconvex case by using the notion of weak subdifferentials. The equivalent formulation of this condition in terms of weak subdifferentials and augmented normal cones is also presented. 相似文献
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Acta Mathematicae Applicatae Sinica, English Series - We consider the problems of minimizing the sum of a continuously differentiable convex function and a nonsmooth convex function in this paper.... 相似文献
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In this paper, we present a nonmonotone algorithm for solving nonsmooth composite optimization problems. The objective function of these problems is composited by a nonsmooth convex function and a differentiable function. The method generates the search directions by solving quadratic programming successively, and makes use of the nonmonotone line search instead of the usual Armijo-type line search. Global convergence is proved under standard assumptions. Numerical results are given. 相似文献
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Generalized Nash equilibrium problems (GNEPs) allow, in contrast to standard Nash equilibrium problems, a dependence of the
strategy space of one player from the decisions of the other players. In this paper, we consider jointly convex GNEPs which
form an important subclass of the general GNEPs. Based on a regularized Nikaido-Isoda function, we present two (nonsmooth)
reformulations of this class of GNEPs, one reformulation being a constrained optimization problem and the other one being
an unconstrained optimization problem. While most approaches in the literature compute only a so-called normalized Nash equilibrium,
which is a subset of all solutions, our two approaches have the property that their minima characterize the set of all solutions
of a GNEP. We also investigate the smoothness properties of our two optimization problems and show that both problems are
continuous under a Slater-type condition and, in fact, piecewise continuously differentiable under the constant rank constraint
qualification. Finally, we present some numerical results based on our unconstrained optimization reformulation. 相似文献
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Guoyin Li Tianxiang Liu Ting Kei Pong 《Computational Optimization and Applications》2017,68(2):407-436
We study the applicability of the Peaceman–Rachford (PR) splitting method for solving nonconvex optimization problems. When applied to minimizing the sum of a strongly convex Lipschitz differentiable function and a proper closed function, we show that if the strongly convex function has a large enough strong convexity modulus and the step-size parameter is chosen below a threshold that is computable, then any cluster point of the sequence generated, if exists, will give a stationary point of the optimization problem. We also give sufficient conditions guaranteeing boundedness of the sequence generated. We then discuss one way to split the objective so that the proposed method can be suitably applied to solving optimization problems with a coercive objective that is the sum of a (not necessarily strongly) convex Lipschitz differentiable function and a proper closed function; this setting covers a large class of nonconvex feasibility problems and constrained least squares problems. Finally, we illustrate the proposed algorithm numerically. 相似文献