最优化是一门应用相当广泛的学科，其理论与算法的研究已相对成熟。而实际应用中，好的算法是有效解决问题的关键，所以对算法的评价与比较尤为重要。以往对优化算法的比较，多是从算法本身的收敛速度、迭代次数及有无大范围收敛等特性进行比较，一般这种评价无法兼顾问题的各个方面，不足以体现算法解决问题的优劣。因此本文提出优化算法的迭代效益、效益均值、效益方差、最优效益。最优化算法的优化效益的研究是一个全新的研究领域，从优化效益的角度来比较算法的优劣。该研究不仅为优化算法提供了有效的评价方式，同时能够用优化效益的观点有效解决实际问题，且具有广泛的应用价值。

首先，概述论文所涉及到的优化理论与优化方法。基于算法评价指标，本文给出算法迭代的优化效益相关定义，提出一种新的算法评价方法。众多优化算法，在求极小值问题中均希望找到目标函数有相当量的下降的方向进行迭代。算法解决问题的优劣与函数值下降的量有着密切的关系，因此提出的优化效益即考虑目标函数值下降量与迭代点步长的关系，优化效益的研究价值在于建立了算法本身与目标函数之间的联系。

其次，利用优化效益对最速下降法、修正牛顿法、共轭梯度法以及拟牛顿法进行评价，通过对每一类算法的迭代数据进行优化效益相关值计算，分别给出以上四类算法在求解单一算例时，算法的优化效益分析；进一步对拟牛顿法、共轭梯度法进行评价，分别给出两类算法在求解多个优化算例时，基于优化效益相关值对两种算法进行优劣比较，通过对结论的分析其结论与实际是相符的，且这种评价方式避免了以往对算法评价的复杂性与局限性。

最后，用优化效益的观点解决两类实际问题，即投资风险问题和高等学校学费制定标准问题，分别在优化效益意义下，在优化问题的求解过程进行优化效益相关值计算，最终得到最优效益意义下问题的最优解。从优化效益观点解决实际问题不仅比以往求解优化问题的方法更简便，同时求解结果更具有实际意义。

Optimization is a widely used subject, its theory and algorithm research has been relatively mature. In practical application, a good algorithm is the key to solve problems effectively, so the evaluation and comparison of algorithms is particularly important. In the past, optimization algorithms were compared in terms of their convergence speed, iteration times and whether there is a large range of convergence. Generally, such evaluation cannot take into account all aspects of the problem, and is not enough to reflect the advantages and disadvantages of the algorithm to solve the problem. Therefore, this paper proposes the definition of optimization benefit, including iterative benefit, mean benefit, benefit variance and optimal benefit. The optimization efficiency of optimization algorithm is a new research field, from the perspective of optimization efficiency to compare the advantages and disadvantages of algorithms. This study not only provides an effective evaluation method for optimization algorithms, but also can effectively solve practical problems with the view of optimization efficiency, and has a wide range of application value.

Firstly, the optimization theory and optimization methods involved in this paper are summarized. The definition of optimization benefit related to algorithm iteration is given, which is mainly proposed based on many optimization algorithms. In the minima problem, we all hope to find the direction of the objective function to iterate with a considerable amount of decline. There is a close relationship between the problem solved by the algorithm and the amount of function value decline. Therefore, the optimization benefit proposed considers the relationship between the value decline of the objective function and the step length of the iteration point, which is essentially an evaluation method of the algorithm. The research value of optimization benefit lies in establishing the relationship between the algorithm itself and the objective function.

Secondly, the optimization benefits are used to evaluate the fastest descent method, the modified Newton method, the conjugate gradient method and the quasi-Newton method, and the iterative data of each algorithm are calculated to evaluate the relative iterative benefits of the above algorithms when only one optimization problem is solved. Furthermore, the quasi-Newton method and conjugate gradient method are evaluated, and the comprehensive iterative benefits of the two algorithms in solving multiple optimization problems are evaluated respectively. Based on the optimization efficiency correlation value, the two algorithms are compared and the conclusion is consistent with the reality. This evaluation method avoids the complexity of the previous algorithm evaluation.

Finally, two kinds of practical problems, namely investment risk problem and college tuition standard problem, are solved from the viewpoint of optimization benefit. In the sense of optimization benefit, the relevant value of optimization benefit is calculated in the process of solving the optimization problem, and finally the optimal solution of the problem in the sense of optimal benefit is obtained. To solve practical problems from the view of optimization efficiency is not only easier than the previous method of solving optimization problems, but also more practical significance.

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