General decay for a viscoelastic Kirchhoff equation with Balakrishnan-Taylor damping, dynamic boundary conditions and a time-varying delay term
Wenjun Liu Biqing Zhu Gang Li Danhua Wang
Evolution Equations & Control Theory 2017, 6(2): 239-260 doi: 10.3934/eect.2017013

In this paper, we consider a viscoelastic Kirchhoff equation with Balakrishnan-Taylor damping, dynamic boundary conditions and a time-varying delay term acting on the boundary. By using the Faedo-Galerkin approximation method, we first prove the well-posedness of the solutions. By introducing suitable energy and perturbed Lyapunov functionals, we then prove the general decay results, from which the usual exponential and polynomial decay rates are only special cases. To achieve these results, we consider the following two cases according to the coefficient α of the strong damping term: for the presence of the strong damping term (α>0), we use the strong damping term to control the time-varying delay term, under a restriction of the size between the time-varying delay term and the strong damping term; for the absence of the strong damping term (α=0), we use the viscoelasticity term to control the time-varying delay term, under a restriction of the size between the time-varying delay term and the kernel function.

keywords: Viscoelastic Kirchhoff equation Balakrishnan-Taylor damping dynamic boundary conditions time-varying delay
A Vlasov-Poisson plasma of infinite mass with a point charge
Gang Li Xianwen Zhang
Kinetic & Related Models 2018, 11(2): 303-336 doi: 10.3934/krm.2018015

We study the time evolution of the three dimensional Vlasov-Poisson plasma interacting with a positive point charge in the case of infinite mass. We prove the existence and uniqueness of the classical solution to the system by assuming that the initial density slightly decays in space, but not integrable. This result extends a previous theorem for Yukawa potential obtained in [10] to the case of Coulomb interaction.

keywords: Vlasov-Poisson plasma point charge infinite mass Coulomb interaction classical solution
Multi-objective optimization algorithm based on improved particle swarm in cloud computing environment
Min Zhang Gang Li
Discrete & Continuous Dynamical Systems - S 2018, 0(0): 1413-1426 doi: 10.3934/dcdss.2019097

In cloud computing environment, in order to optimize the deployment scheduling of resources, it is necessary to improve the accuracy of the optimal solution, guarantee the convergence ability of the algorithm, and improve the performance of cloud computing. In this paper, a multi-objective optimization algorithm based on improved particle swarm is proposed. A multi-objective optimization model is built. Improved multi-scale particle swarm is used to optimize the built multi-objective model. The combination of the global search capability and the local search capability of the algorithm is realized by using Gaussian variation operator with varied scales. The large scale Gaussian variation operator with concussion characteristics can complete fast global search for decision space, so that particles can quickly locate the surrounding area of the optimal solution, which enhances the ability to escape the local optimal solution of the algorithm and avoids the occurrence of precocious convergence. The small scale variation operator gradually reduces the area near the optimal solution. Experimental results show that the improved particle swarm optimization algorithm can effectively improve the precision of the optimal solution and ensure the convergence of the algorithm.

keywords: Cloud computing environment improved particle swarm multi-objective optimization algorithm
The stable duality of DC programs for composite convex functions
Gang Li Lipu Zhang Zhe Liu
Journal of Industrial & Management Optimization 2017, 13(1): 63-79 doi: 10.3934/jimo.2016004

In this paper, we consider a composite DC optimization problem with a cone-convex system in locally convex Hausdorff topological vector spaces. By using the properties of the epigraph of the conjugate functions, some necessary and sufficient conditions which characterize the strong Fenchel-Lagrange duality and the stable strong Fenchel-Lagrange duality are given. We apply the results obtained to study the minmax optimization problem and $l_1$ penalty problem.

keywords: Strong Fenchel-Lagrange duality DC programming stable duality
Stable strong and total parametrized dualities for DC optimization problems in locally convex spaces
Gang Li Xiaoqi Yang Yuying Zhou
Journal of Industrial & Management Optimization 2013, 9(3): 671-687 doi: 10.3934/jimo.2013.9.671
By using properties of dualizing parametrization functions, Lagrangian functions and the epigraph technique, some sufficient and necessary conditions of the stable strong duality and strong total duality for a class of DC optimization problems are established.
keywords: epigraph Conjugate functions DC programming.
Time consistent policy of multi-period mean-variance problem in stochastic markets
Zhiping Chen Jia Liu Gang Li
Journal of Industrial & Management Optimization 2016, 12(1): 229-249 doi: 10.3934/jimo.2016.12.229
Due to the non-separability of the variance operator, the optimal investment policy of the multi-period mean-variance model in Markovian markets doesn't satisfy the time consistency. We propose a new weak time consistency in stochastic markets and show that the pre-commitment optimal policy satisfies the weak time consistency at any intermediate period as long as the investor's wealth is no more than a specific threshold. When the investor's wealth exceeds the threshold, the weak time consistency no longer holds. In this case, by modifying the pre-commitment optimal policy, we derive a wealth interval, from which we determine a more efficient revised policy. The terminal wealth obtained under this revised policy can achieve the same mean as, but not greater variance than those of the terminal wealth obtained under the pre-commitment optimal policy; a series of superior investment policies can be obtained depending on the degree the investor wants the conditional variance to decrease. It is shown that, in the above revising process, a positive cash flow can be taken out of the market. Finally, an empirical example illustrates our theoretical results. Our results generalize existing conclusions for the multi-period mean-variance model in deterministic markets.
keywords: policy revision. Markovian markets Bellman's optimality principle mean-variance Time inconsistency

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