A new trust region algorithm for solving convex LC 1 optimization problem is presented.It is proved that the algorithm is globally convergent and the rate of convergence is superlinear under some reasonable assum...A new trust region algorithm for solving convex LC 1 optimization problem is presented.It is proved that the algorithm is globally convergent and the rate of convergence is superlinear under some reasonable assumptions.展开更多
This paper presents a trust region two phase model algorithm for solving the equality and bound constrained nonlinear optimization problem. A concept of substationary point is given. Under suitable assumptions,the gl...This paper presents a trust region two phase model algorithm for solving the equality and bound constrained nonlinear optimization problem. A concept of substationary point is given. Under suitable assumptions,the global convergence of this algorithm is proved without assuming the linear independence of the gradient of active constraints. A numerical example is also presented.展开更多
In this paper, we propose a homotopy continuous method (HCM) for solving a weak efficient solution of multiobjective optimization problem (MOP) with feasible set unbounded condition, which is arising in Economical Dis...In this paper, we propose a homotopy continuous method (HCM) for solving a weak efficient solution of multiobjective optimization problem (MOP) with feasible set unbounded condition, which is arising in Economical Distributions, Engineering Decisions, Resource Allocations and other field of mathematical economics and engineering problems. Under the suitable assumption, it is proved to globally converge to a weak efficient solution of (MOP), if its x-branch has no weak infinite solution.展开更多
The recurrent neural network （RNN） model based on projective operator was studied. Different from the former study, the value region of projective operator in the neural network in this paper is a general closed con...The recurrent neural network （RNN） model based on projective operator was studied. Different from the former study, the value region of projective operator in the neural network in this paper is a general closed convex subset of n-dimensional Euclidean space and it is not a compact convex set in general, that is, the value region of projective operator is probably unbounded. It was proved that the network has a global solution and its solution trajectory converges to some equilibrium set whenever objective function satisfies some conditions. After that, the model was applied to continuously differentiable optimization and nonlinear or implicit complementarity problems. In addition, simulation experiments confirm the efficiency of the RNN.展开更多
In this paper, we present m time secant like multi projection algorithm for sparse unconstrained minimization problem. We prove this method are all q superlinearly convergent to the solution about m≥1 . At last, we f...In this paper, we present m time secant like multi projection algorithm for sparse unconstrained minimization problem. We prove this method are all q superlinearly convergent to the solution about m≥1 . At last, we from some numerical results, discuss how to choose the number m to determine the approximating matrix properly in practical use.展开更多
A QP-free, truncated hybrid (QPFTH) method was proposed and developed in [6] forsolving sparse large-scale nonlinear programming problems. In the hybrid method, a truncatedNewton method is combined with the method of ...A QP-free, truncated hybrid (QPFTH) method was proposed and developed in [6] forsolving sparse large-scale nonlinear programming problems. In the hybrid method, a truncatedNewton method is combined with the method of multiplier. In every iteration level, either atruncated solution for a symmetric system of linear equations is determined by CG algorithmor an unconstrained subproblem is solved by the limited memory BFGS algorithm such thatthe hybrid algorithm is suitable to large-scale problems. In this paper, the consistency in thehybrid method and a steplength procedure are discussed and developed. The global convergenceof QPFTH method is proved and the two-step Q-quadratic convergence rate is further analyzed.展开更多
基金Supported by the National Natural Science Foundation of P.R.China(1 9971 0 0 2 ) and the Subject ofBeijing Educational Committ
文摘A new trust region algorithm for solving convex LC 1 optimization problem is presented.It is proved that the algorithm is globally convergent and the rate of convergence is superlinear under some reasonable assumptions.
文摘This paper presents a trust region two phase model algorithm for solving the equality and bound constrained nonlinear optimization problem. A concept of substationary point is given. Under suitable assumptions,the global convergence of this algorithm is proved without assuming the linear independence of the gradient of active constraints. A numerical example is also presented.
文摘In this paper, we propose a homotopy continuous method (HCM) for solving a weak efficient solution of multiobjective optimization problem (MOP) with feasible set unbounded condition, which is arising in Economical Distributions, Engineering Decisions, Resource Allocations and other field of mathematical economics and engineering problems. Under the suitable assumption, it is proved to globally converge to a weak efficient solution of (MOP), if its x-branch has no weak infinite solution.
文摘The recurrent neural network （RNN） model based on projective operator was studied. Different from the former study, the value region of projective operator in the neural network in this paper is a general closed convex subset of n-dimensional Euclidean space and it is not a compact convex set in general, that is, the value region of projective operator is probably unbounded. It was proved that the network has a global solution and its solution trajectory converges to some equilibrium set whenever objective function satisfies some conditions. After that, the model was applied to continuously differentiable optimization and nonlinear or implicit complementarity problems. In addition, simulation experiments confirm the efficiency of the RNN.
文摘In this paper, we present m time secant like multi projection algorithm for sparse unconstrained minimization problem. We prove this method are all q superlinearly convergent to the solution about m≥1 . At last, we from some numerical results, discuss how to choose the number m to determine the approximating matrix properly in practical use.
文摘A QP-free, truncated hybrid (QPFTH) method was proposed and developed in [6] forsolving sparse large-scale nonlinear programming problems. In the hybrid method, a truncatedNewton method is combined with the method of multiplier. In every iteration level, either atruncated solution for a symmetric system of linear equations is determined by CG algorithmor an unconstrained subproblem is solved by the limited memory BFGS algorithm such thatthe hybrid algorithm is suitable to large-scale problems. In this paper, the consistency in thehybrid method and a steplength procedure are discussed and developed. The global convergenceof QPFTH method is proved and the two-step Q-quadratic convergence rate is further analyzed.
