尹江华1,2,3,4, 简金宝2, 江羡珍2
尹江华, 简金宝, 江羡珍. 凸约束非光滑方程组一个新的谱梯度投影算法[J]. 计算数学, 2020, 42(4): 457-471.
Yin Jianghua, Jian Jinbao, Jiang Xianzhen. A SPECTRAL GRADIENT PROJECTION ALGORITHM FOR CONVEX CONSTRAINED NONSMOOTH EQUATIONS BASED ON AN ADAPTIVE LINE SEARCH[J]. Mathematica Numerica Sinica, 2020, 42(4): 457-471.
Yin Jianghua1,2,3,4, Jian Jinbao2, Jiang Xianzhen2
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[1] Ortega J M, Rheinboldt W C. Iterative solution of nonlinear equations in several variables[M]. New York:Academic Press, 1970.[2] Sun D F, Womersley R S, Qi H D. A feasible semismooth asymptotically Newton method for mixed complementarity problems[J]. Mathematical Programming, 2002, 94(1):167-187.[3] Tong X J, Zhou S Z. A smoothing projected Newton-type method for semismooth equations with bound constraints[J]. Journal of Industrial and Management Optimization, 2005, 1(2):235-250.[4] Wang C W, Wang Y J, Xu C L. A projection method for a system of nonlinear monotone equations with convex constraints[J]. Mathematical Methods of Operations Research, 2007, 66(1):33-46.[5] Qi L Q, Tong X J, Li D H. Active-set projected trust-region algorithm for box-constrained nonsmooth equations[J]. Journal of Optimization Theory and Applications, 2004, 120(3):601-625.[6] Fan J Y. On the Levenberg-Marquardt methods for convex constrained nonlinear equations[J]. Journal of Industrial and Management Optimization, 2013, 9(1):227-241.[7] Yu Z S, Lin J, Sun J, Xiao Y H, Liu L Y, Li Z H. Spectral gradient projection method for monotone nonlinear equations with convex constraints[J]. Applied Numerical Mathematics, 2009, 59(10):2416-2423.[8] Sun M, Liu J. New hybrid conjugate gradient projection method for the convex constrained equations[J]. Calcolo, 2016, 53(3):399-411.[9] Ding Y Y, Xiao Y H, Li J W. A class of conjugate gradient methods for convex constrained monotone equations[J]. Optimization, 2017, 66(12):2309-2328.[10] Solodov M V, Svaiter B F. A globally convergent inexact Newton method for systems of monotone equations[C]//In:Fukushima M, Qi L. (eds.), Reformulation:Piecewise Smooth, Semi-smooth and Smoothing Methods, Norwell:Kluwer Academic Publishers, 1998, 355-369.[11] Barzilai J M, Borwein M. Two-point step size gradient methods[J]. IMA Journal of Numerical Analysis, 1988, 8(1):141-148.[12] Li Q, Li D H. A class of derivative-free methods for large-scale nonlinear monotone equations[J]. IMA Journal of Numerical Analysis, 2011, 31(4):1625-1635.[13] 吴晓云, 周学良. 凸约束非线性方程组的一种无导数投影方法[J]. 数学的实践与认识, 2018, 48(2):119-126.[14] Amini K, Kamandi A. A new line search strategy for finding separating hyperplane in projectionbased methods[J]. Numerical Algorithms, 2015, 70(3):559-570.[15] 许琼, 林海婵, 欧宜贵. 带凸约束的非线性方程组的无导数记忆法[J]. 应用数学,2016, 29(3):686-696.[16] Zarantonello E H. Projections on convex sets in hilbert space and spectral theory[M]. New York:Academic Press, 1971.[17] Dolan E D, Moré J J. Benchmarking optimization software with performance profiles[J]. Mathematical programming, 2002, 91(2):201-213. |
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