A study on inequality dualization method for decision making and optimization problems

2016 Fiscal Year Final Research Report

• Project/Area Number: 26400207
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: Akita Prefectural University
• Principal Investigator: Yutaka Kimura 秋田県立大学, システム科学技術学部, 教授 (10315616)
• Project Period (FY): 2014-04-01 – 2017-03-31
• Keywords: 双対化 / 意思決定 / 最適化 / 2次計画

Outline of Final Research Achievements

In this research, we propose some dualization methods and investigate a mutual relationship between optimal points and optimal values for a class of quadratic programming problems, which include problems with decision making and optimization. We have discussed over and over again how to derive dual problems from primal problems and vice versa. And we have succeeded in deriving three dualization methods which are called dynamic dualization, plus-minus dualization, and inequality dualization. Moreover, it is shown that the optimal solutions for quadratic programming problem are characterized by the Fibonacci numbers or the Golden number. We have established some duality theorems for quadratic programming problem, which are called Fibonacci complementary duality, Golden complementary duality, and so on.

Free Research Field

最適化理論