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 exis...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.展开更多
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 functi...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.展开更多
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 ...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.展开更多
基金Supported by National Natural Science Foundation of China(62103169,51875380)China Postdoctoral Science Foundation(2021M691313)。
文摘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.
文摘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.
基金supported by National Key R&D Program of China (Grant No. 2021YFA1003100)supported by National Natural Science Foundation of China (Grant Nos. 11825101, 11522101, and 11431013)+1 种基金supported by the Talent Fund of Beijing Jiaotong Universitysupported by China Postdoctoral Science Foundation (Grant Nos. BX20230402 and 2023M743719)。
文摘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.
