论文标题
正规化的Barzilai-Borwein方法
Regularized Barzilai-Borwein method
论文作者
论文摘要
我们基于\ bb方法开发了一个新颖的步骤大小，该方法有效地解决了一些具有挑战性的优化问题，称为正则化\ bb（rbb）步骤。我们指出，RBB STEPIZE是$ \ ell_ {2}^{2} $的紧密解决方案 - 正则化最小二乘问题。当正规项目消失时，rbb逐步降低到原始\ bb台阶。 rbb Stepize包括一类有效的步骤尺寸，例如\ bb spepize的另一个版本。相应的RBB算法的全局收敛性在解决凸二次优化问题中得到了证明。提出了一种适应性生成正则化参数的方案，称为自适应两步参数。增强的RBB步骤用于更有效地解决二次和一般优化问题。在许多条件不足的优化问题中，RBB STEPIZE可以克服BB步骤的不稳定性。此外，在数值实验中，RBB STEPSIZE比BB步骤更强大。数值示例显示了使用所提出的步骤生动地解决一些具有挑战性的优化问题的优点。
We develop a novel stepsize based on \BB method for solving some challenging optimization problems efficiently, named regularized \BB (RBB) stepsize. We indicate that RBB stepsize is the close solution to a $\ell_{2}^{2}$-regularized least squares problem. When the regularized item vanishes, the RBB stepsize reduces to the original \BB stepsize. RBB stepsize includes a class of valid stepsizes, such as another version of \BB stepsize. The global convergence of the corresponding RBB algorithm is proved in solving convex quadratic optimization problems. One scheme for adaptively generating regularization parameters was proposed, named adaptive two-step parameter. An enhanced RBB stepsize is used for solving quadratic and general optimization problems more efficiently. RBB stepsize could overcome the instability of BB stepsize in many ill-conditioned optimization problems. Moreover, RBB stepsize is more robust than BB stepsize in numerical experiments. Numerical examples show the advantage of using the proposed stepsize to solve some challenging optimization problems vividly.
