In this paper,we propose a variable metric method for unconstrained multiobjective optimization problems(MOPs).First,a sequence of points is generated using different positive definite matrices in the generic framewor...In this paper,we propose a variable metric method for unconstrained multiobjective optimization problems(MOPs).First,a sequence of points is generated using different positive definite matrices in the generic framework.It is proved that accumulation points of the sequence are Pareto critical points.Then,without convexity assumption,strong convergence is established for the proposed method.Moreover,we use a common matrix to approximate the Hessian matrices of all objective functions,along which a new nonmonotone line search technique is proposed to achieve a local superlinear convergence rate.Finally,several numerical results demonstrate the effectiveness of the proposed method.展开更多
This paper explores the convergence of a class of optimally conditioned self scaling variable metric (OCSSVM) methods for unconstrained optimization. We show that this class of methods with Wolfe line search are glob...This paper explores the convergence of a class of optimally conditioned self scaling variable metric (OCSSVM) methods for unconstrained optimization. We show that this class of methods with Wolfe line search are globally convergent for general convex functions.展开更多
基金the Major Program of the National Natural Science Foundation of China(Nos.11991020 and 11991024)the National Natural Science Foundation of China(Nos.11971084 and 12171060)+1 种基金the Natural Science Foundation of Chongqing(No.cstc2019jcyj-zdxmX0016)Foundation of Chongqing Normal University(Nos.22XLB005 and 22XLB006).
文摘In this paper,we propose a variable metric method for unconstrained multiobjective optimization problems(MOPs).First,a sequence of points is generated using different positive definite matrices in the generic framework.It is proved that accumulation points of the sequence are Pareto critical points.Then,without convexity assumption,strong convergence is established for the proposed method.Moreover,we use a common matrix to approximate the Hessian matrices of all objective functions,along which a new nonmonotone line search technique is proposed to achieve a local superlinear convergence rate.Finally,several numerical results demonstrate the effectiveness of the proposed method.
文摘This paper explores the convergence of a class of optimally conditioned self scaling variable metric (OCSSVM) methods for unconstrained optimization. We show that this class of methods with Wolfe line search are globally convergent for general convex functions.
