BIG HANKEL OPERATORS ON HARDY SPACES OF STRONGLY PSEUDOCONVEX DOMAINS

In this article,we investigate the(big) Hankel operator H_(f) on the Hardy spaces of bounded strongly pseudoconvex domains Ω in C^(n).We observe that H_(f ) is bounded on H~p(Ω)(1 <p <∞) if f belongs to BMO and we obtain some characterizations for Hf on H^(2)(Ω) of other pseudoconvex domains.In these arguments,Amar's L^(p)-estimations and Berndtsson's L^(2)-estimations for solutions of the ■_(b)-equation play a crucial role.In addition,we solve Gleason's problem for Hardy spaces H^(p)(Ω)(1 ≤p≤∞) of bounded strongly pseudoconvex domains.

Singular integral on bounded strictly pseudoconvex domain

Kytmanov and Myslivets gave a special Cauchy principal value of the singular integral on the bounded strictly pseudoconvex domain with smooth boundary. By means of this Cauchy integral principal value, the corresponding singular integral and a composition formula are obtained. This composition formula is quite different from usual ones in form. As an application, the corresponding singular integral equation and the system of singular integral equations are discussed as well.

Multiobjective Nonlinear Symmetric Duality Involving Generalized Pseudoconvexity

The purpose of this paper is to introduce second order (K, F)-pseudoconvex and second order strongly (K, F)- pseudoconvex functions which are a generalization of cone-pseudoconvex and strongly cone-pseudoconvex functions. A pair of second order symmetric dual multiobjective nonlinear programs is formulated by using the considered functions. Furthermore, the weak, strong and converse duality theorems for this pair are established. Finally, a self duality theorem is given.

Random gradient-free method for online distributed optimization with strongly pseudoconvex cost functions

This paper focuses on the online distributed optimization problem based on multi-agent systems. In this problem, each agent can only access its own cost function and a convex set, and can only exchange local state information with its current neighbors through a time-varying digraph. In addition, the agents do not have access to the information about the current cost functions until decisions are made. Different from most existing works on online distributed optimization, here we consider the case where the cost functions are strongly pseudoconvex and real gradients of the cost functions are not available. To handle this problem, a random gradient-free online distributed algorithm involving the multi-point gradient estimator is proposed. Of particular interest is that under the proposed algorithm, each agent only uses the estimation information of gradients instead of the real gradient information to make decisions. The dynamic regret is employed to measure the proposed algorithm. We prove that if the cumulative deviation of the minimizer sequence grows within a certain rate, then the expectation of dynamic regret increases sublinearly. Finally, a simulation example is given to corroborate the validity of our results.

Boundary points, minimal L^(2) integrals and concavity property Ⅱ: Weakly pseudoconvex Kähler manifolds

In this paper, we consider minimal L^(2) integrals on the sublevel sets of plurisubharmonic functions on weakly pseudoconvex K?hler manifolds with Lebesgue measurable gain related to modules at boundary points of the sublevel sets, and establish a concavity property of the minimal L^(2) integrals. As applications, we present a necessary condition for the concavity degenerating to linearity, a concavity property related to modules at inner points of the sublevel sets, an optimal support function related to modules, a strong openness property of modules and a twisted version, and an effectiveness result of the strong openness property of modules.

Zeroth-Order Methods for Online Distributed Optimization with Strongly Pseudoconvex Cost Functions

This paper studies an online distributed optimization problem over multi-agent systems.In this problem,the goal of agents is to cooperatively minimize the sum of locally dynamic cost functions.Different from most existing works on distributed optimization,here we consider the case where the cost function is strongly pseudoconvex and real gradients of objective functions are not available.To handle this problem,an online zeroth-order stochastic optimization algorithm involving the single-point gradient estimator is proposed.Under the algorithm,each agent only has access to the information associated with its own cost function and the estimate of the gradient,and exchange local state information with its immediate neighbors via a time-varying digraph.The performance of the algorithm is measured by the expectation of dynamic regret.Under mild assumptions on graphs,we prove that if the cumulative deviation of minimizer sequence grows within a certain rate,then the expectation of dynamic regret grows sublinearly.Finally,a simulation example is given to illustrate the validity of our results.

一种解决带有凸集约束的分布式伪凸优化的连续时间算法

本文提出了一种可以解决带有凸集约束且全局目标函数是非光滑伪凸的分布式优化问题的连续时间算法.本文所提出的分布式优化算法采用罚函数方法建模,通过构造一个合适的惩罚项迫使所有智能体的状态变量进入可行域.通过使用李雅普诺夫(有限时间)稳定性理论等工具,证明了在一定假设下,本文所提出的算法将在有限时间内达成一致状态且进入可行域并永驻其中,并在此之后收敛到原分布式优化问题的最优解集.此外,该算法在运行时各个智能体仅仅需要接收邻居节点的相对状态的符号信息.最后,仿真结果验证了本文所提出的算法的有效性.

一种基于罚函数法解决非光滑伪凸优化问题的神经网络算法及其应用

针对实际应用中遇到的非光滑伪凸优化问题,本文提出一种创新的解决方案——结合罚函数理念和微分包含理论的单层神经网络算法。首先,通过数学理论证明,本文算法能够使状态解最终收敛至伪凸优化问题的最优解,从而确立所提出算法的正确性;其次,通过对2个数值实验的模拟收敛结果进行分析,进一步验证算法的有效性;最后,用本文算法解决实际应用问题,展示其在解决伪凸优化问题上的实际应用价值。与现有的神经网络算法相比,本文算法不仅能够解决更一般的具有凸不等式和等式约束的伪凸优化问题,也可以解决实际应用问题。此外,本文算法层次结构简单,无需计算精确的罚参数,可以选取任意初始点,无需添加任何辅助变量,为伪凸优化问题的解决提供一种有效途径。

Plurigenera of compact connected strongly pseudoconvex CR manifolds In memory of Salah Baouendi

Strongly pseudoconvex CR manifolds are boundaries of Stein varieties with isolated normal singularities.We introduce a series of new invariant plurigeneraδm,m∈Z+for a strongly pseudoconvex CR manifold.The main purpose of this paper is to present the following result:Let X1and X2be two compact strongly pseudoconvex embeddable CR manifolds of dimension 2n-1 3.If there is a non-constant CR morphism from X1to X2,thenδm(X2)δm(X1)whereδm(Xi)is the plurigeneus of Xi(see Definition 2.4).

Concavity of minimal L^(2) integrals related to multiplier ideal sheaves on weakly pseudoconvex Kahler manifolds

In this paper,we present the concavity of the minimal L^(2)integrals related to multiplier ideal sheaves on the weakly pseudoconvex Kahler manifolds,which implies the sharp effectiveness results of the strong openness conjecture and a conjecture posed by Demailly and Kollar(2001)on weakly pseudoconvex Kahler manifolds.We obtain the relation between the concavity and the L^(2)extension theorem.

On Iterates of Holomorphic Maps in Strongly Pseudoconvex Domains

The theory of iterates of holomorphic maps is a very active topic in recent years. The well-known Denjoy-Wolff theorem characterized the asymptotic behavior of the iterate sequences of holomorphic self-maps in the unit disc △C. Subsequent authors extended this theorem to some special domains of C^n(n】1). Briefly speaking, the research

Non-isotropic weighted L^p estimates for the -equation on piecewise smooth strictly pseudoconvex domains

In this paper we obtain non-isotropic weighted Lp estimates with the boundary distance weight function for the-equation on piecewise smooth strictly pseudoconvex domains under a hypoth- esis of complex transversality in Cn using the explicit formula of solutions by Berndtsson-Andersson.

Bergman type operators on a class of weakly pseudoconvex domains

A necessary and sufficient condition for the boundedness of the operator: $(T_{s,u,u} f)(\xi ) = h^{u + \tfrac{v}{a}} (\xi )\smallint _{\Omega _a } h^s (\xi ')K_{s,u,v} (\xi ,\xi ')f(\xi ')dv(\xi ') on L^p (\Omega _a ,dv_\lambda ),1< p< \infty $ , is obtained, where $\Omega _a = \left\{ {\xi = (z,w) \in \mathbb{C}^{n + m} :z \in \mathbb{C}^n ,w \in \mathbb{C}^m ,|z|^2 + |w|^{2/a}< 1} \right\},h(\xi ) = (1 - |z|^2 )^a - |w|^2 $ andK x,u,v (ξ,ξ′).This generalizes the works in literature from the unit ball or unit disc to the weakly pseudoconvex domain ω a . As an appli cation, it is proved thatf?L H p (ω a ,dv λ) implies $h\tfrac{{|a|}}{a} + |\beta |(\xi )D_2^a D_z^\beta f \in L^p (\Omega _a ,dv_\lambda ),1 \leqslant p< \infty $ , for any multi-indexa=(α1,?,α n and ? = (?1, —?). An interesting question is whether the converse holds.

q-PSEUDOCONVEX DOMAIN IN γ-COMPLETE MANIFOLD

In this article we always assume r+q≤n, otherwise the result is trivial. Now we introduce some definitions and notations.Definition 1. Suppose D is a connected open subset in an n-dimensional complex manifold with C^2-boundary. We say function φ is a defining function of if there exists an open neighborhood U of x such that φ: U→R and D ∩ U={y∈M|φ(y)【0},

THE -PROBLEM FOR HOLOMORPHIC (0,2)-FORMS ON PSEUDOCONVEX DOMAINS IN SEPARABLE HILBERT SPACES AND D.F.N. SPACES

This paper shows that the 8-problem for holomorphic (0, 2)-forms on Hubert spaces is solv-able on pseudoconvex open subsets. By using this result, the authors investigate the existence of the solution of the -equation for holomorphic (0, 2)-forms on pseudoconvex domains in D.F.N. spaces.

THE EXPLICIT SOLUTIONS OF C_(p,q)^(k+α)-FORM FOR THE -EQUATIONS ON PSEUDOCONVEX OPEN SETS

In this paper, we study the integral solution operators for the -equations on pseudoconvex domains. As a generalization of [1] for the -dequations on pseudoconvex domains with boundary of class C∞, we obtain the explicit integral operator solutions of C -form for the -equations on pseudoconvex open sets with boundary of Ck (k≥0) and the sup-norm estimates of which solutions have similar as that [1] in form.

新型单层递归神经网络解决非光滑伪凸优化问题的研究

非光滑伪凸优化问题广泛应用于科学及工程等领域,属于一类特殊的非凸优化问题,具有重要的研究意义.针对含有等式约束和不等式约束条件的非光滑伪凸优化问题,该文提出了一种新的神经动力学方法,并引入罚函数和正则化思想.通过有效的罚函数保证了所提出的神经网络状态的有界性,从而保证神经网络的状态解在有限时间内进入可行域中,最终收敛到原问题的最优解.最后,用两个数值实验验证了所提出模型的有效性.与现有的神经网络相比,该文的模型有以下优势:避免预先计算精确的惩罚因子,初始点的选取无特殊要求,结构简单.

一种解决分布式伪凸优化问题的神经网络模型

针对带有凸不等式约束的分布式伪凸优化问题,基于微分包含思想,提出了一种分布式神经网络模型。该模型根据目标函数与约束条件构造罚函数,使得每个分布式节点能在有限时间内进入可行域且不再离开,最终达成一致并收敛到原始优化问题的最优解。最后,通过2个仿真实验验证了分布式神经网络模型的有效性和准确性。与现有的神经网络模型相比,该模型结构简单,能够解决伪凸问题,并且不需要精确的计算罚参数。

有界平衡拟凸域上一类具有参数表示的映照类

设Ω是Cn 中具有C2 定义函数的有界平衡拟凸域 ,在Ω上引进一个双全纯映照子族———具有参数表示的映照族 ,研究其一些性质 :包括增长定理、掩盖定理 ,得到其与星形映照同型的增长定理及掩盖定理 .

递归神经网络方法解决非光滑伪凸优化问题

针对目标函数为非光滑伪凸函数且带有等式约束和不等式约束的优化问题,基于罚函数以及微分包含的思想,构建一个层次仅为一层且不包含惩罚算子的新型递归神经网络模型.该模型不用提前计算惩罚参数,能够很好地收敛.理论证明全局解存在,模型的状态解能够在有限的时间内进到原目标函数的可行域并不再离开,其状态解最终收敛到目标函数的一个最优解.仿真实验证实了理论结果的可行性.