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该文研究了一类非光滑半定规划问题,其中目标函数是C1,1函数,约束是半定的. 借助于Peano广义梯度,给出了其二阶最优性必要条件和二阶最优性充分条件 相似文献
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本文利用函数局部逼近导出一个不利用目标函数二阶导数的一维优化方法.我们证明了该方法的二阶收敛性.我们给出的数值结果表明该方法和牛顿法的计算表现十分相似. 相似文献
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引进了一种二阶切导数,借助该切导数给出了变序结构集值优化问题取得局部弱非控点的二阶最优性必要条件.在某种特殊情况下,给出了一阶最优性条件.通过修正的Dubovitskij-Miljutin切锥导出的约束规格,给出了两个集值映射之和的二阶相依切导数的关系式,进一步得到目标函数与变锥函数的二阶相依切导数分开形式的最优性必要条件. 相似文献
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主要讨论了无约束最优化中非线性最小二乘问题的收敛性.侧重于收敛的速率和整体、局部分析.改变了Gauss—Newton方法收敛性定理的条件,分两种情况证明了:(1)目标函数的海赛矩阵正定(函数严格凸)时为强整体二阶收敛;(2)目标函数不保证严格凸性,但海赛矩阵的逆存在时为局部收敛,敛速仍为二阶,同时给出了J(X)~(-1)和Q(X)~(-1)之间存在、有界性的等价条件. 相似文献
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给出并证明了函数在一点处广义二阶可导的一个充分条件,分析了二元函数在一点的广义二阶导数和二阶混合偏导数之间的关系. 相似文献
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梯度投影法是一类有效的约束最优化算法,在最优化领域中占有重要的地位.但是,梯度投影法所采用的投影是正交投影,不包含目标函数和约束函数的二阶导数信息·因而;收敛速度不太令人满意.本文介绍一种共轭投影概念,利用共轭投影构造了一般线性或非线性约束下的共轭投影变尺度算法,并证明了算法在一定条件下具有全局收敛性.由于算法中的共轭投影恰当地包含了目标函数和约束函数的二阶导数信息,因而收敛速度有希望加快.数值试验的结果表明算法是有效的. 相似文献
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基于一个自协调指数核函数, 设计求解二阶锥规划的原始-对偶内点算法. 根据自协调指数核函数的二阶导数与三阶导数的特殊关系, 在求解问题的中心路径时, 用牛顿方向代替了负梯度方向来确定搜索方向. 由于自协调指数核函数不具有``Eligible'性质, 在分析算法的迭代界时, 利用牛顿方法求解目标函数满足自协调性质的无约束优化问题的技术, 估计算法内迭代中自协调指数核函数确定的障碍函数的下降量, 得到原始-对偶内点算法大步校正的迭代界O(2N\frac{\log2N}{\varepsilon}), 这里N是二阶锥的个数. 这个迭代界与线性规划情形下的迭代界一致. 最后, 通过数值算例验证了算法的有效性. 相似文献
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《Optimization》2012,61(3):193-209
In this paper, we study regularity and optimality conditions for the BLPP by using a marginal function formulation, where the marginal function is defined by the optimal value function of the lower problem. We address the regularity issue by exploring the structure of the tangent cones of the feasible set of the BLPP. These regularity results indicate that the nonlinear/nonlinear BLPP is most likely degenerate and a class of nonlinear/linear BLPP is regular in the conventional sense. Existence of exact penalty function is proved for a class of nonlinear/linear BLPP. Fritz-John type optimality conditions are derived for nonlinear BLPP, while KKT type conditions are obtained for a class of nonlinear/linear BLPP in the framework of nonsmooth analysis. A typical example is examined for these conditions and some applications of these conditions are pointed out 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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In this paper, Mond-Weir’s type dual in programming problem with an interval-valued objective function and interval-valued inequality constrict conditions is formulated. Duality theorems are established under suitable conditions. A real-valued Lagrangian function for the interval-valued programming is defined. Further, the saddle point of Lagrangian function is also defined and saddle point optimality conditions are presented. 相似文献
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Optimality conditions are derived for a nonlinear fractional program in which a support function appears in the numerator and denominator of the objective function as well as in each constraint function. As an application of these optimality conditions, a dual to this program is formulated and various duality results are established under generalized convexity. Several known results are deduced as special cases. 相似文献
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《Annals of Pure and Applied Logic》2014,165(7-8):1339-1351
We give necessary and sufficient conditions on a non-oscillatory curve in an o-minimal field such that, for any bounded definable function, the germ of the function on an initial segment of the curve has a definable extension to a closed set. This situation is translated into a question about types: What are the conditions on an n-type such that, for any bounded definable function, the germ of the function on the type has a definable continuous global extension? Certain categories of definable types have this property, and we give the precise conditions that are equivalent to existence of the global extension. 相似文献
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We generalize the D-gap function developed in the literature for variational inequalities to a general equilibrium problem (EP). Through the D-gap function, the equilibrium problem is cast as an unconstrained minimization problem. We give conditions under which any stationary point of the D-gap function is a solution of EP and conditions under which it provides a global error bound for EP. Finally, these results are applied to box-constrained EP and then weaker conditions are established to obtain the desired results for box-constrained EP. 相似文献
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O. G. Avsyankin 《Mathematical Notes》2018,104(3-4):331-338
Sufficient conditions for the compactness in generalized Morrey spaces of the composition of a convolution operator and the operator of multiplication by an essentially bounded function are obtained. Very weak conditions on the function are also obtained under which the commutator of the operator of multiplication by such a function and a convolution operator is compact. The compactness of convolution operators in domains of cone type is investigated. 相似文献
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大多数随机延迟微分方程数值解的结果是在全局Lipschitz条件下获得的.许多延迟方程不满足全局Lipschitz条件,研究非全局Lipschitz条件下的数值解的性质,具有重要的意义.本文证明了漂移系数满足单边Lipschitz条件和多项式增长条件,扩散系数满足全局Lipschitz条件的一类随机延迟微分方程的Eul... 相似文献
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讨论了具有离散参数的绕积马氏链的中心极限定理,给出了加在过程样本函数上充分条件。得到了绕积马氏链的中心极限定理成立的充分条件. 相似文献