A harmonic framework for stepsize selection in gradient methods
研究了在非线性无约束优化问题的梯度方法中，使用逆调和瑞利商与目标值来选择步长，提供了一个参数化现有步长方案的灵活框架，并提出了新的步长族，包括对自适应Barzilai-Borwein方法的扩展。
Abstract We study the use of inverse harmonic Rayleigh quotients with target for the stepsize selection in gradient methods for nonlinear unconstrained optimization problems. This not only provides an elegant and flexible framework to parametrize and reinterpret existing stepsize schemes, but it also gives inspiration for new flexible and tunable families of steplengths. In particular, we analyze and extend the adaptive Barzilai–Borwein method to a new family of stepsizes. While this family exploits negative values for the target, we also consider positive targets. We present a convergence analysis for quadratic problems extending results by Dai and Liao (IMA J Numer Anal 22(1):1–10, 2002), and carry out experiments outlining the potential of the approaches.