Global Optimization Models on Industrial Systems and Efficient Approaches for Solving them

工业系统全局优化模型及其有效解决方法

• 批准号: 10450041
• 负责人: KONNO Hiroshi
• 金额: $ 4.29万
• 依托单位: Tokyo Institute of Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 1998
• 资助国家: 日本
• 起止时间: 1998 至 1999
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10450041/
• 关键词: industrial system; global optimization; non-convex quadratic programming; internationally diversified investment; non-convex programming; fractional function programming; combinatorial optimization; enumeration problems; 分数計画問題; 組み合わせ最適化; 大域的最適化

Our results can be classified roughly to models of global optimization and non-convex programming. For the former, we proposed a large scale internationally diversified investment model that can drastically speed up solving optimal portfolio problems without. increasing numerical errors.For the latter, we proposed efficient algorithms for solving non-convex quadratic programming, non-convex programming with objective functions which are products or sum of fractional functions. For low rank non-convex quadratic programming, we also proposed a fast algorithm obtained by combining heuristic methods and branch and cut method. These can solve problems that can not be solved in usual way.For portfolio optimization problems with concave transaction costs and network flow problems with concave costs, we proposed fast branch and bound algorithms. These problems are very practical.Combinatorial problems are one of non-convex programming problems. We improved several enumeration algorithms for matchings and directed or undirected spanning trees.

我们的结果可以大致分为全局优化模型和非凸规划模型。对于前者，我们提出了一个大规模的国际多元化投资模型，可以大大加快解决最优投资组合问题，没有。对于后者，提出了求解非凸二次规划、目标函数为分式函数乘积或和的非凸规划的有效算法.对于低秩非凸二次规划问题，我们还提出了一个结合启发式方法和分支割法的快速算法。这些可以解决通常方法无法解决的问题。对于具有凹交易成本的投资组合优化问题和具有凹成本的网络流问题，我们提出了快速分支定界算法。组合规划问题是一类非凸规划问题。我们改进了几个匹配和有向或无向生成树的枚举算法。

项目成果

Takeaki UNO: "A New Approach for Speeding Up Enumeration Algorithm an Its Application for Matroid Bases"Lecture Note in Computer Science 1627. Springer-Verlag. 349-359 (1999)

Takeaki UNO：“加速枚举算法的新方法及其在拟阵基中的应用”计算机科学讲义 1627。Springer-Verlag。

Konno H.and N.Abe: "Minimization of the sum of Three Linear Fractional Functions"Journal on Global Optimizations. 15. (1999)

Konno H. 和 N.Abe：“三个线性分数函数之和的最小化”全局优化杂志。

今野 浩: "理財工学II : 数理計画法による資産運用最適化" 日科技連出版社, 145 (1998)

Hiroshi Konno：“金融科学与工程 II：使用数学编程优化资产管理” Nikkei Ren Shuppansha，145 (1998)

Kuno T., Kanuo H. and Ine A.: "A Peterministic Approach to Linear Programs with Several Additional Multiplicative Constraints"Computational Optimization and Application. 14. 347-366 (1999)

Kuno T.、Kanuo H. 和 Ine A.：“带有几个附加乘法约束的线性规划的 Peterministic 方法”计算优化和应用。

Konno, H. and H. Yamashita: "Minimization of the Sum and the Product of Several Linear Fractional Functions over a polytope"Naval Research Logistics. 583-591 (1999)

Konno, H. 和 H. Yamashita：“多面体上多个线性分数函数的和与积的最小化”海军研究后勤。