STUDIES ON CONTINUOUS OPTIMIZATION PROBLEMS AND THEIR DISCRETIZATION

1、实现了“非线性规划问题的共轭点理论”的主要目标。也就是说，我们定义了非线性规划问题的Jacobi方程、共轭点、严格共轭点和Riccati方程。我们已经用(严格)共轭点的形式描述了最优性。此外，我们还阐明了Riccati方程的解与Hesse矩阵支点的关系。2.证明了模糊环境下随机系统的决策过程问题可以用一种基于不变嵌入原理的递推方法来求解。通过这项研究，岩本在2001年被授予第八届贝尔曼连续奖最佳论文奖。此外，我们还将一类新的评价方法和动态规划方法引入了不确定条件下的数理金融学。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、给出了一个不含斯莱特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、提出了一种从具有动态噪声的混沌时间序列中估计嵌入维度和延迟时间的方法。在上述研究的基础上，我们在国际研讨会上做了18次演讲，在国内会议上做了42次演讲。此外，已发表或正在出版的文章有39篇。

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).