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J. Barzilai, J. M. Borwein. Two-point step size gradient methods. IMA J. Numer. Anal, 1988, 8(1): 141-148.

被以下文章引用:

• 标题: 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

  作者: 牛善洲, 王义, 崔丹丹

  关键字: 边界约束优化, 投影梯度方法, 非单调线搜索, 全局收敛性 Bound Constrained Optimization; Projected Gradient Method; Nonmonotone Line Search; Global Convergence

  期刊名称: 《Pure Mathematics》, Vol.1 No.1, 2011-04-15

  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。 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.