STUDIES ON CONTINUOUS OPTIMIZATION PROBLEMS AND THEIR DISCRETIZATION

连续优化问题及其离散化研究

基本信息

批准号：
11440033
负责人：
KAWASAKI Hidefumi
金额：
$ 2.56万
依托单位：
KYUSHU UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
1999
资助国家：
日本
起止时间：
1999 至 2001
项目状态：
已结题

项目摘要

1, We have achieved the main goal "conjugate point theory for nonlinear programming problems". Namely, we have defined the Jacobi equation, conjugate points, strict conjugate points, and the Riccati equation for the nonlinear programming problems. We have described the optimality in terms of (strict) conjugate points. Furthermore, we have clarified the relationship between the solution of the Riccati equation and the pivots of the Hesse matrix. This research takes the lead in this area.2, We have shown that decision process problems on the stochastic system under the fuzzy environment can be solved by a new recurrent method based on the invariant embedding principle. By this research, Iwamoto was awarded the Best Paper Award of the 8th Bellman Continuum in 2001. Also, we have introduced a new class of evaluations and dynamic programming methods into the mathematical finance under uncertainty. Furthermore, we proposed a primitive strategy that includes historical data of states and decisions for the class.3, We have proposed a method to convert the maximum eigen-value problem of a positive reciprocal matrix in AHP into a convex programming problem, and we have proved the existence of the optimal solution.4, We have given a KKT condition for a multiobjective convex programming problem without Slater's condition. Furthermore, we have shown the continuity of the epsilon- efficient set and the efficient set.5, We have proposed a method that estimates the embedding dimension and delay time from chaotic time series with dynamic noise. On the above researches, we gave 18 lectures in international symposiums and 42 talks in domestic conferences. Furthermore, 39 articles were published or are (in press).

1、我们已经实现了“非线性规划问题的共轭点理论”的主要目标。即，我们定义了非线性规划问题的雅可比方程、共轭点、严格共轭点和Riccati方程。我们已经用（严格）共轭点描述了最优性。此外，我们还阐明了Riccati方程的解与Hesse矩阵的主元之间的关系。本研究在该领域处于领先地位。2、我们证明了模糊环境下随机系统的决策过程问题可以通过一种新的基于不变嵌入原理的递归方法来解决。通过这项研究，岩本获得了2001年第八届贝尔曼连续体最佳论文奖。此外，我们还向不确定性下的数学金融引入了一类新的评估和动态规划方法。此外，我们提出了一种原始策略，其中包括该类的状态和决策的历史数据。 3、我们提出了一种将 AHP 中正倒数矩阵的最大特征值问题转换为凸规划问题的方法，并且我们有证明了最优解的存在性。4、给出了无Slater条件的多目标凸规划问题的KKT条件。此外，我们还证明了epsilon有效集和有效集的连续性。5、我们提出了一种从带有动态噪声的混沌时间序列中估计嵌入维数和延迟时间的方法。在上述研究方面，我们在国际研讨会上做了18次报告，在国内会议上做了42次报告。此外，已发表或正在出版的文章有 39 篇。