STUDIES ON CONTINUOUS OPTIMIZATION PROBLEMS AND THEIR DISCRETIZATION

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Jacobi方程、共轭点、严格共轭点和Riccati方程。我们用（严格的）共轭点描述了最优性。进一步阐明了Riccati方程的解与Hesse矩阵的支点之间的关系。这项研究在这个领域处于领先地位。我们证明了在模糊环境下随机系统上的决策过程问题可以用一种基于不变嵌入原理的递归方法求解。通过这项研究，Iwamoto在2001年获得了第八届Bellman Continuum的最佳论文奖。同时，我们还在不确定条件下的数学金融中引入了一类新的评价方法和动态规划方法。此外，我们提出了一个原始策略，该策略包含了类的状态和决策的历史数据。提出了一种将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，并证明了其最优解的存在性。给出了不带Slater条件的多目标凸规划问题的KKT条件。进一步证明了有效集与有效集的连续性。提出了一种从含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。在上述研究中，我们在国际学术会议上做了18次报告，在国内会议上做了42次报告。此外，已发表或正在（印刷中）发表39篇文章。

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).