A trust-region algorithm is presented for a nonlinear optimization problem of equality-constraints. The characterization of the algorithm is using inexact gradient information. Global convergence results are demonstra...A trust-region algorithm is presented for a nonlinear optimization problem of equality-constraints. The characterization of the algorithm is using inexact gradient information. Global convergence results are demonstrated where the gradient values are obeyed a simple relative error condition.展开更多
The paper develops the local convergence of Inexact Newton-Like Method(INLM)for approximating solutions of nonlinear equations in Banach space setting.We employ weak Lipschitz and center-weak Lipschitz conditions to p...The paper develops the local convergence of Inexact Newton-Like Method(INLM)for approximating solutions of nonlinear equations in Banach space setting.We employ weak Lipschitz and center-weak Lipschitz conditions to perform the error analysis.The obtained results compare favorably with earlier ones such as[7,13,14,18,19].A numerical example is also provided.展开更多
随着人工智能对算力需求的激增,数据中心(internet data center,IDC)作为数据处理与存储的机构,其能耗需求远超预期,使用新能源是其可持续发展的需要。然而,可再生能源具有出力不确定性,仅依靠数据中心参与需求响应难以实现消纳,可配置...随着人工智能对算力需求的激增,数据中心(internet data center,IDC)作为数据处理与存储的机构,其能耗需求远超预期,使用新能源是其可持续发展的需要。然而,可再生能源具有出力不确定性,仅依靠数据中心参与需求响应难以实现消纳,可配置储能提高系统灵活性。因此,本工作建立了以规划总成本最优为目标的数据中心与电池储能(battery energy storage,BES)协同规划两阶段鲁棒模型,为防止规划结果过于乐观,引入了储能寿命约束。同时针对在求解所建模型过程中,传统C&CG(column-and-constraint generation)算法存在难以平衡求解速度与精度间关系的问题,本工作提出了一种不精确列和生成约束算法i-C&CG(inexact column-and-constraint generation)进行求解。基于IEEE30节点与IEEE118节点算例系统进行优化解算,仿真结果表明,与仅配置单一储能相比,本工作所提模型储能年等效建设成本下降39785元,数据中心年等效建设成本下降289080元;且本工作所提算法与传统C&CG相比,采用0.18低精度下的i-C&CG,与采用0.16较高精度的C&CG相比较,i-C&CG最多可缩短3632 s的单次迭代求解所需时间,且最终计算结果的相对误差为0.46%,两者收敛间隙与相对最优间隙近似。展开更多
As a generalization of the two-term conjugate gradient method(CGM),the spectral CGM is one of the effective methods for solving unconstrained optimization.In this paper,we enhance the JJSL conjugate parameter,initiall...As a generalization of the two-term conjugate gradient method(CGM),the spectral CGM is one of the effective methods for solving unconstrained optimization.In this paper,we enhance the JJSL conjugate parameter,initially proposed by Jiang et al.(Computational and Applied Mathematics,2021,40:174),through the utilization of a convex combination technique.And this improvement allows for an adaptive search direction by integrating a newly constructed spectral gradient-type restart strategy.Then,we develop a new spectral CGM by employing an inexact line search to determine the step size.With the application of the weak Wolfe line search,we establish the sufficient descent property of the proposed search direction.Moreover,under general assumptions,including the employment of the strong Wolfe line search for step size calculation,we demonstrate the global convergence of our new algorithm.Finally,the given unconstrained optimization test results show that the new algorithm is effective.展开更多
Numerical treatment of engineering application problems often eventually results in a solution of systems of linear or nonlinear equations.The solution process using digital computational devices usually takes tremend...Numerical treatment of engineering application problems often eventually results in a solution of systems of linear or nonlinear equations.The solution process using digital computational devices usually takes tremendous time due to the extremely large size encountered in most real-world engineering applications.So,practical solvers for systems of linear and nonlinear equations based on multi graphic process units（GPUs）are proposed in order to accelerate the solving process.In the linear and nonlinear solvers,the preconditioned bi-conjugate gradient stable（PBi-CGstab）method and the Inexact Newton method are used to achieve the fast and stable convergence behavior.Multi-GPUs are utilized to obtain more data storage that large size problems need.展开更多
文摘A trust-region algorithm is presented for a nonlinear optimization problem of equality-constraints. The characterization of the algorithm is using inexact gradient information. Global convergence results are demonstrated where the gradient values are obeyed a simple relative error condition.
文摘The paper develops the local convergence of Inexact Newton-Like Method(INLM)for approximating solutions of nonlinear equations in Banach space setting.We employ weak Lipschitz and center-weak Lipschitz conditions to perform the error analysis.The obtained results compare favorably with earlier ones such as[7,13,14,18,19].A numerical example is also provided.
文摘随着人工智能对算力需求的激增,数据中心(internet data center,IDC)作为数据处理与存储的机构,其能耗需求远超预期,使用新能源是其可持续发展的需要。然而,可再生能源具有出力不确定性,仅依靠数据中心参与需求响应难以实现消纳,可配置储能提高系统灵活性。因此,本工作建立了以规划总成本最优为目标的数据中心与电池储能(battery energy storage,BES)协同规划两阶段鲁棒模型,为防止规划结果过于乐观,引入了储能寿命约束。同时针对在求解所建模型过程中,传统C&CG(column-and-constraint generation)算法存在难以平衡求解速度与精度间关系的问题,本工作提出了一种不精确列和生成约束算法i-C&CG(inexact column-and-constraint generation)进行求解。基于IEEE30节点与IEEE118节点算例系统进行优化解算,仿真结果表明,与仅配置单一储能相比,本工作所提模型储能年等效建设成本下降39785元,数据中心年等效建设成本下降289080元;且本工作所提算法与传统C&CG相比,采用0.18低精度下的i-C&CG,与采用0.16较高精度的C&CG相比较,i-C&CG最多可缩短3632 s的单次迭代求解所需时间,且最终计算结果的相对误差为0.46%,两者收敛间隙与相对最优间隙近似。
基金supported by the National Natural Science Foundation of China(No.72071202)the Key Laboratory of Mathematics and Engineering Applications,Ministry of Education。
文摘As a generalization of the two-term conjugate gradient method(CGM),the spectral CGM is one of the effective methods for solving unconstrained optimization.In this paper,we enhance the JJSL conjugate parameter,initially proposed by Jiang et al.(Computational and Applied Mathematics,2021,40:174),through the utilization of a convex combination technique.And this improvement allows for an adaptive search direction by integrating a newly constructed spectral gradient-type restart strategy.Then,we develop a new spectral CGM by employing an inexact line search to determine the step size.With the application of the weak Wolfe line search,we establish the sufficient descent property of the proposed search direction.Moreover,under general assumptions,including the employment of the strong Wolfe line search for step size calculation,we demonstrate the global convergence of our new algorithm.Finally,the given unconstrained optimization test results show that the new algorithm is effective.
文摘Numerical treatment of engineering application problems often eventually results in a solution of systems of linear or nonlinear equations.The solution process using digital computational devices usually takes tremendous time due to the extremely large size encountered in most real-world engineering applications.So,practical solvers for systems of linear and nonlinear equations based on multi graphic process units（GPUs）are proposed in order to accelerate the solving process.In the linear and nonlinear solvers,the preconditioned bi-conjugate gradient stable（PBi-CGstab）method and the Inexact Newton method are used to achieve the fast and stable convergence behavior.Multi-GPUs are utilized to obtain more data storage that large size problems need.
