论文标题
为Barzilai-Borwein方法配备二维二次终止属性
Equipping Barzilai-Borwein method with two dimensional quadratic termination property
论文作者
论文摘要
一个新颖的梯度步骤Zize是出于将Barzilai-Borwein（BB）方法带有二维二次终止特性的动机。新型步骤的一个显着特征是，其计算仅取决于以前的迭代中的BB步骤尺寸，并且不需要任何确切的线路搜索或Hessian，因此很容易将其扩展以进行非线性优化。通过自适应采取长度BB步骤和与新步骤大小相关的一些短步骤，我们开发了一种有效的梯度方法来进行二次优化和一般不受约束的优化，并将其扩展为解决极端特征值问题。提出的方法进一步扩展，以通过合并梯度投影技术来进行框受限的优化和单线性框架约束的优化。数值实验表明，所提出的方法优于文献中最成功的梯度方法。
A novel gradient stepsize is derived at the motivation of equipping the Barzilai-Borwein (BB) method with two dimensional quadratic termination property. A remarkable feature of the novel stepsize is that its computation only depends on the BB stepsizes in previous iterations and does not require any exact line search or the Hessian, and hence it can easily be extended for nonlinear optimization. By adaptively taking long BB steps and some short steps associated with the new stepsize, we develop an efficient gradient method for quadratic optimization and general unconstrained optimization and extend it to solve extreme eigenvalues problems. The proposed method is further extended for box-constrained optimization and singly linearly box-constrained optimization by incorporating gradient projection techniques. Numerical experiments demonstrate that the proposed method outperforms the most successful gradient methods in the literature.
