期刊文献+
共找到3篇文章
< 1 >
每页显示 20 50 100
The Rate of Convergence of Augmented Lagrangian Method for Minimax Optimization Problems with Equality Constraints
1
作者 Yu-Hong Dai Li-Wei Zhang 《Journal of the Operations Research Society of China》 EI CSCD 2024年第2期265-297,共33页
The augmented Lagrangian function and the corresponding augmented Lagrangian method are constructed for solving a class of minimax optimization problems with equality constraints.We prove that,under the linear indepen... The augmented Lagrangian function and the corresponding augmented Lagrangian method are constructed for solving a class of minimax optimization problems with equality constraints.We prove that,under the linear independence constraint qualification and the second-order sufficiency optimality condition for the lower level problem and the second-order sufficiency optimality condition for the minimax problem,for a given multiplier vectorμ,the rate of convergence of the augmented Lagrangian method is linear with respect to||μu-μ^(*)||and the ratio constant is proportional to 1/c when the ratio|μ-μ^(*)||/c is small enough,where c is the penalty parameter that exceeds a threshold c_(*)>O andμ^(*)is the multiplier corresponding to a local minimizer.Moreover,we prove that the sequence of multiplier vectors generated by the augmented Lagrangian method has at least Q-linear convergence if the sequence of penalty parameters(ck)is bounded and the convergence rate is superlinear if(ck)is increasing to infinity.Finally,we use a direct way to establish the rate of convergence of the augmented Lagrangian method for the minimax problem with a quadratic objective function and linear equality constraints. 展开更多
关键词 Minimax optimization Augmented Lagrangian method Rate of convergence Second-order sufficiency optimality
原文传递
On Some Aspects of Perturbation Analysis for Matrix Cone Optimization Induced by Spectral Norm
2
作者 Shao-Yan Guo Li-Wei Zhang Shou-Lin Hao 《Journal of the Operations Research Society of China》 EI CSCD 2015年第3期275-296,共22页
In this paper,we consider a cone problem of matrix optimization induced by spectral norm(MOSN).By Schur complement,MOSN can be reformulated as a nonlinear semidefinite programming(NLSDP)problem.Then we discuss the con... In this paper,we consider a cone problem of matrix optimization induced by spectral norm(MOSN).By Schur complement,MOSN can be reformulated as a nonlinear semidefinite programming(NLSDP)problem.Then we discuss the constraint nondegeneracy conditions and strong second-order sufficient conditions of MOSN and its SDP reformulation,and obtain that the constraint nondegeneracy condition of MOSN is not always equivalent to that of NLSDP.However,the strong second-order sufficient conditions of these two problems are equivalent without any assumption.Finally,a sufficient condition is given to ensure the nonsingularity of the Clarke’s generalized Jacobian of the KKT system for MOSN. 展开更多
关键词 Spectral norm Negative semidefinite cone Strong second-order sufficient condition Constraint nondegeneracy condition
原文传递
A Note on B-Subdifferential of Projection Operator on Polyhedral Set
3
作者 Hao-Yang Liu Jia Wu Li-Wei Zhang 《Journal of the Operations Research Society of China》 EI 2024年第3期837-845,共9页
This note characterizes the set of Fréchet-differentiable points of the projection operator on a polyhedral set and the B-subdifferential of this projection operator at any point.
关键词 Polyhedral set Projection operator B-subdifferential Strong regularity
原文传递
上一页 1 下一页 到第
使用帮助 返回顶部