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中文摘要：
最陡峭的降下方法是为优化的最简单的坡度方法。沿着每个最陡峭的降下方向的准确的线搜索可以很慢慢地收敛，是众所周知的。重要结果被 Barzilar 和 Borwein 给，它被证明是 superlinearlyconvergent 为凸在二个维的空格二次，并且为高维的问题表现相当好。BB 方法不是单调，这样除非某些非单调技术正在被使用，为一般非线性的功能被概括不是容易的。因此，发现启用快集中并且拥有单调性质的步骤尺寸公式是很合乎需要的。为最陡峭的降下方法的如此的步骤尺寸α _ κ在这篇论文被建议。有在甚至重复的这种新步骤尺寸和在奇怪的重复的准确的线搜索的 Analgorithm 被建议。数字结果被介绍，它证实新方法能为二个维的问题在 3 重复以内发现准确答案。新方法为小规模问题是很有效的。新方法的一个修改版本也被介绍，在为选择步尺寸的新技术在每二准确的线搜索以后被使用的地方。修改算法为小规模问题比得上为大规模问题并且更好的 Barzilar-Borwein 方法。
英文摘要：
The steepest descent method is the simplest gradient method for optimization. It is well known that exact line searches along each steepest descent direction may converge very slowly. An important result was given by Barzilar and Borwein, which is proved to be superlinearly convergent for convex quadratic in two dimensional space, and performs quite well for high dimensional problems. The BB method is not monotone, thus it is not easy to be generalized for general nonlinear functions unless certain non-monotone techniques being applied. Therefore, it is very desirable to find stepsize formulae which enable fast convergence and possess the monotone property. Such a stepsize αk for the steepest descent method is suggested in this paper. An algorithm with this new stepsize in even iterations and exact line search in odd iterations is proposed. Numerical results are presented, which confirm that the new method can find the exact solution within 3 iteration for two dimensional problems. The new method is very efficient for small scale problems. A modified version of the new method is also presented, where the new technique for selecting the stepsize is used after every two exact line searches. The modified algorithm is comparable to the Barzilar-Borwein method for large scale problems and better for small scale problems.
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