STUDIES ON CONTINUOUS OPTIMIZATION PROBLEMS AND THEIR DISCRETIZATION

连续优化问题及其离散化研究

• 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
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-11440033/
• 关键词: conjugate point; Jacobi equation; Riccati equation; variational problem; nonlinear programming; dynamic programming; fazzy optimization; convex programming; ファジィ最適化; 非線形計画問題; 動的計画; 不変埋没原理; パラメトリック最適化; ファジィ; カオス性; 変分法; 微分不可能計画; 逆理論

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、实现了“非线性规划问题的共扼点理论”的主要目标。也就是说，我们已经定义了Jacobi方程，共轭点，严格共轭点，和Riccati方程的非线性规划问题。我们已经描述了（严格）共轭点的最优性。进一步阐明了Riccati方程的解与黑森矩阵的枢轴之间的关系。本文的研究在这一领域处于领先地位。2、我们证明了模糊环境下随机系统的决策过程问题可以用一种新的基于不变嵌入原理的递归方法来求解。通过这项研究，岩本在2001年获得了第八届贝尔曼连续体最佳论文奖。同时，我们还将一类新的评价方法和动态规划方法引入到不确定条件下的数理金融中。3、提出了将AHP中正互反矩阵的最大特征值问题转化为凸规划问题的方法，并证明了最优解的存在性。4、给出了不含斯莱特条件的多目标凸规划问题的KKT条件。进一步证明了混沌时间序列的有效集和非有效集的连续性。5、提出了一种估计含动态噪声混沌时间序列的嵌入维数和延迟时间的方法。在上述研究中，我们在国际研讨会上发表了18篇演讲，在国内会议上发表了42篇演讲。此外，39篇文章已经发表或正在出版。

项目成果

S. Iwamoto: "Recursive method in stochastic optimization under compound criteria"Advances in Math. Economics. 3. 63-82 (2001)

S. Iwamoto：“复合标准下随机优化的递归方法”数学进展。

S. Shiraishi: "Sensitivity analysis and nonsmooth analysis of nonlinear programming problems"in Proceedings of the 11^<th> RAMP symp.. 97-105 (1999)

S. Shiraishi：“非线性规划问题的敏感性分析和非平滑分析”，第 11 届 RAMP symp.. 97-105 (1999) 论文集

S. Shiraishi: "On regularity of maxim and in Danskin's formula (Japanese)"RIMS Kokyuroku. 11144. 42-45 (1999)

S. Shiraishi：“论格言的规律性和 Danskin 公式（日语）”RIMS Kokyuroku。

S. Iwamoto and T. Fujita: "Markov decision process with fractional-Type criteria (Japanese)"RIMS Kokyuroku. 1015. 153-163 (1999)

S. Iwamoto 和 T. Fujita：“采用分数型标准的马尔可夫决策过程（日语）”RIMS Kokyuroku。

H.Kawasaki: "A Conjugate points theory for a nonlinear programming problems"Proceedings of the International Conference on NACA2001. (to appear).

H.Kawasaki：“非线性规划问题的共轭点理论”NACA2001 国际会议论文集。