边界约束优化问题一个新的投影梯度方法
A New Projected Gradient Method for Bound Constrained Optimization
摘要: 投影梯度法因其算法简单、易于实现，非常适合求解大规模优化问题。本文基于拟柯西方程和对角变换，构造了一个新的投影梯度算法。在非单调线搜索条件下，证明该方法具有全局收敛性。最后数值实验表明新方法是有效的。
Abstract: The projected gradient method is very suitable for solving large-scale nonlinear programming due to the simplicity of its iteration and implement. In this paper, combined with the quasi-Cauchy equation and diagonal updating, a new projected gradient method is proposed for bound constrained optimization. On the basis of nonmonotone line search, global convergence is established. The numerical results show that the new algorithm is promising.
文章引用：牛善洲, 王义, 崔丹丹. 边界约束优化问题一个新的投影梯度方法[J]. 理论数学, 2011, 1(1): 46-50. http://dx.doi.org/10.12677/pm.2011.11010

参考文献

[1] R. H. Byrd, P. Lu, J. Nocedal. A limited-memory algorithm for bound constrained optimization. SIAM J. Sci. Stat. Com-put,
[2] 1995, 16(5): 1190-1208.
[3] W. W. Hager, H. Zhang. A new active set algorithm for box constrained optimization. SIAM J. Optim, 2006, 17(2): 526- 557.
[4] J. Moré, G. Toraldo. On the solution of large scale quadratic programming problem with bound constrains. SIAM J. Optim, 1991, 1(1): 93-113.
[5] Z. S. Yu, Sun J, Qin Y. A multivariate spectral projected gradient method for bound constrained optimization. J. Comput. Appl. Math, 2011, 235(8): 2263-2269.
[6] E. G. Birgin, G. M. Martinez, M. Raydan. Nonmonotone spectral projected gradient methods on convex sets. SIAM J. Optim, 2000, 10(4): 1196-1211.
[7] J. Barzilai, J. M. Borwein. Two-point step size gradient methods. IMA J. Numer. Anal, 1988, 8(1): 141-148.
[8] R. Andreani, E. G. Birgin, J. M. Martínez, et al. Spectral projected gradient and variable metric methods for optimization with linear inequalities. IMA J. Numer. Anal, 2005, 25(2): 221-252.
[9] E. G. Birgin, G. M. Marttínez. Larges-scale active-set box- constrained optimization method with spectral projected gradients. Comput. Optim Appl, 2002, 23(1): 101-125.
[10] Y. Dai, R. Fletcher. Projected Barzilai-Borwein method for large-scale box-constrained quadratic programming. Numer. Math, 2005, 100(1): 21-47.
[11] W. J. Leong, M. A. Hassan, M. Farid. A monotone gradient method via weak secant equation for unconstrained optimization. Taiwanese J. Math, 2010, 14(2): 413- 423.
[12] L. Han, G. Yu, L. Guan. Multivariate spectral gradient method for unconstrained optimization. Appl Math Comput, 2008, 201(1-2): 621-630.
[13] L. Grippo, F. Lampariello, S. Licidis. A nonmonotone line search technique for Newtons method. SIAM Journal on Numerical Analysis, 1986, 23(4): 26-33.

为你推荐