非单调Armijo型线搜索的有效性
On efficiency of nonmonotone Armijo-type line searches
摘要：
单调性和非单调性在研究非线性最优化中迭代格式的整体收敛和效率方面起着关键作用。本文讨论了下降计划的一些特点和背后的动机非单调策略，并研究了Armijo型线搜索配备了一些流行的非单调条款的效率。更具体地说，我们提出了两个新的非单调项，将它们结合到Armijo规则中，并建立了由这些方案产生的序列的整体收敛。此外，我们报告了大量的数值结果和比较表明的非单调Armijo型线搜索使用最流行的搜索方向解决无约束最优化问题的性能。最后，我们利用所考虑的非单调计划来解决信号和图像处理中出现的一个重要的逆问题。
英文摘要：
Monotonicity and nonmonotonicity play a key role in studying the global convergence and the efficiency of iterative schemes employed in the field of nonlinear optimization, where globally convergent and computationally efficient schemes are explored. This paper addresses some features of descent schemes and the motivation behind nonmonotone strategies and investigates the efficiency of an Armijo-type line search equipped with some popular nonmonotone terms. More specifically, we propose two novel nonmonotone terms, combine them into Armijo's rule and establish the global convergence of sequences generated by these schemes. Furthermore, we report extensive numerical results and comparisons indicating the performance of the nonmonotone Armijo-type line searches using the most popular search directions for solving unconstrained optimization problems. Finally, we exploit the considered nonmonotone schemes to solve an important inverse problem arising in signal and image processing.
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