A New Projected Gradient Method for Bound Constrained Optimization
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 (2011) 边界约束优化问题一个新的投影梯度方法。 理论数学， 1， 46-50. doi: 10.12677/pm.2011.11010
 R. H. Byrd, P. Lu, J. Nocedal. A limited-memory algorithm for bound constrained optimization. SIAM J. Sci. Stat. Com-put,
 1995, 16(5): 1190-1208.
 W. W. Hager, H. Zhang. A new active set algorithm for box constrained optimization. SIAM J. Optim, 2006, 17(2): 526- 557.
 J. Moré, G. Toraldo. On the solution of large scale quadratic programming problem with bound constrains. SIAM J. Optim, 1991, 1(1): 93-113.
 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.
 E. G. Birgin, G. M. Martinez, M. Raydan. Nonmonotone spectral projected gradient methods on convex sets. SIAM J. Optim, 2000, 10(4): 1196-1211.
 J. Barzilai, J. M. Borwein. Two-point step size gradient methods. IMA J. Numer. Anal, 1988, 8(1): 141-148.
 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.
 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.
 Y. Dai, R. Fletcher. Projected Barzilai-Borwein method for large-scale box-constrained quadratic programming. Numer. Math, 2005, 100(1): 21-47.
 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.
 L. Han, G. Yu, L. Guan. Multivariate spectral gradient method for unconstrained optimization. Appl Math Comput, 2008, 201(1-2): 621-630.
 L. Grippo, F. Lampariello, S. Licidis. A nonmonotone line search technique for Newtons method. SIAM Journal on Numerical Analysis, 1986, 23(4): 26-33.