This paper deals with extensions of higher-order optimality conditions for scalar optimization to multiobjective optimization.A type of directional derivatives for a multiobjective function is proposed,and with this n...This paper deals with extensions of higher-order optimality conditions for scalar optimization to multiobjective optimization.A type of directional derivatives for a multiobjective function is proposed,and with this notion characterizations of strict local minima of order k for a multiobjective optimization problem with a nonempty set constraint are established,generalizing the corresponding scalar case obtained by Studniarski[3].Also necessary not sufficient and sufficient not necessary optimality conditions for this minima are derived based on our directional derivatives,which are generalizations of some existing scalar results and equivalent to some existing multiobjective ones.Many examples are given to illustrate them there.展开更多
针对现有土石坝渗流监控指标拟定方法存在主观性较强和精度较低的不足,基于智能算法改进的超阈值(peaks over threshold,POT)模型,提出了优化的土石坝渗流监控指标拟定方法.以3σ准则为确定最优阈值的理论基础,采用基于混沌映射、结合L...针对现有土石坝渗流监控指标拟定方法存在主观性较强和精度较低的不足,基于智能算法改进的超阈值(peaks over threshold,POT)模型,提出了优化的土石坝渗流监控指标拟定方法.以3σ准则为确定最优阈值的理论基础,采用基于混沌映射、结合Levy飞行和逆向学习的动态选择策略改进的麻雀搜索算法(improved chaos sparrow search algorithm,ICSSA),对POT模型中阈值的选取方法进行优化.建立了ICSSA-POT模型,实现对监测资料尾部数据的拟合,从而得到更为合理的土石坝渗流监控指标.研究表明,相比于传统方法,所提方法可有效避免主观性与随机误差,得到的监测资料尾部数据的拟合决定系数提高了5%,具有更高的计算精度,拟定的渗流监控指标更偏于安全,对防范土石坝渗流破坏、确保土石坝安全长效运行具有较强的指导意义.展开更多
In this paper,an adaptive cubic regularisation algorithm based on affine scaling methods(ARCBASM)is proposed for solving nonlinear equality constrained programming with nonnegative constraints on variables.From the op...In this paper,an adaptive cubic regularisation algorithm based on affine scaling methods(ARCBASM)is proposed for solving nonlinear equality constrained programming with nonnegative constraints on variables.From the optimality conditions of the problem,we introduce appropriate affine matrix and construct an affine scaling ARC subproblem with linearized constraints.Composite step methods and reduced Hessian methods are applied to tackle the linearized constraints.As a result,a standard unconstrained ARC subproblem is deduced and its solution can supply sufficient decrease.The fraction to the boundary rule maintains the strict feasibility(for nonnegative constraints on variables)of every iteration point.Reflection techniques are employed to prevent the iterations from approaching zero too early.Under mild assumptions,global convergence of the algorithm is analysed.Preliminary numerical results are reported.展开更多
In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to ...In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to obtain the maximal positive definite solution of nonlinear matrix equation X+A^(*)X|^(-α)A=Q with the case 0<α≤1.Based on this method,a new iterative algorithm is developed,and its convergence proof is given.Finally,two numerical examples are provided to show the effectiveness of the proposed method.展开更多
针对耦合神经P系统利用脉冲机制实现区域生长依赖于初始种子点选择的问题,提出一种自适应区域生长耦合神经P系统(adaptive region growing coupled neural P systems,ARGCNP)的图像分割方法。该方法利用金豺优化算法(golden jackal opti...针对耦合神经P系统利用脉冲机制实现区域生长依赖于初始种子点选择的问题,提出一种自适应区域生长耦合神经P系统(adaptive region growing coupled neural P systems,ARGCNP)的图像分割方法。该方法利用金豺优化算法(golden jackal optimization,GJO)的全局搜索能力,通过引入四种策略提升GJO的全局寻优性能,从而在图像中寻找最佳阈值点,以优化区域生长中的种子点选择。在实验中,首先通过CEC2017测试函数对改进后的GJO进行性能测试,结果表明改进后的GJO在测试函数上整体性能第一;随后将ARGCNP应用于分割彩色图像和医学图像,以峰值信噪比等三个指标对分割效果进行量化评价,分割结果显示该方法能够提升分割精度及分割结果的稳定性,证明ARGCNP在应用场景下具有的优势,能够满足图像分割需求。展开更多
文摘This paper deals with extensions of higher-order optimality conditions for scalar optimization to multiobjective optimization.A type of directional derivatives for a multiobjective function is proposed,and with this notion characterizations of strict local minima of order k for a multiobjective optimization problem with a nonempty set constraint are established,generalizing the corresponding scalar case obtained by Studniarski[3].Also necessary not sufficient and sufficient not necessary optimality conditions for this minima are derived based on our directional derivatives,which are generalizations of some existing scalar results and equivalent to some existing multiobjective ones.Many examples are given to illustrate them there.
基金Supported by the National Natural Science Foundation of China(12071133)Natural Science Foundation of Henan Province(252300421993)Key Scientific Research Project of Higher Education Institutions in Henan Province(25B110005)。
文摘In this paper,an adaptive cubic regularisation algorithm based on affine scaling methods(ARCBASM)is proposed for solving nonlinear equality constrained programming with nonnegative constraints on variables.From the optimality conditions of the problem,we introduce appropriate affine matrix and construct an affine scaling ARC subproblem with linearized constraints.Composite step methods and reduced Hessian methods are applied to tackle the linearized constraints.As a result,a standard unconstrained ARC subproblem is deduced and its solution can supply sufficient decrease.The fraction to the boundary rule maintains the strict feasibility(for nonnegative constraints on variables)of every iteration point.Reflection techniques are employed to prevent the iterations from approaching zero too early.Under mild assumptions,global convergence of the algorithm is analysed.Preliminary numerical results are reported.
基金Supported in part by Natural Science Foundation of Guangxi(2023GXNSFAA026246)in part by the Central Government's Guide to Local Science and Technology Development Fund(GuikeZY23055044)in part by the National Natural Science Foundation of China(62363003)。
文摘In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to obtain the maximal positive definite solution of nonlinear matrix equation X+A^(*)X|^(-α)A=Q with the case 0<α≤1.Based on this method,a new iterative algorithm is developed,and its convergence proof is given.Finally,two numerical examples are provided to show the effectiveness of the proposed method.
文摘针对耦合神经P系统利用脉冲机制实现区域生长依赖于初始种子点选择的问题,提出一种自适应区域生长耦合神经P系统(adaptive region growing coupled neural P systems,ARGCNP)的图像分割方法。该方法利用金豺优化算法(golden jackal optimization,GJO)的全局搜索能力,通过引入四种策略提升GJO的全局寻优性能,从而在图像中寻找最佳阈值点,以优化区域生长中的种子点选择。在实验中,首先通过CEC2017测试函数对改进后的GJO进行性能测试,结果表明改进后的GJO在测试函数上整体性能第一;随后将ARGCNP应用于分割彩色图像和医学图像,以峰值信噪比等三个指标对分割效果进行量化评价,分割结果显示该方法能够提升分割精度及分割结果的稳定性,证明ARGCNP在应用场景下具有的优势,能够满足图像分割需求。
