The development of fast algorithm for solving linear programming started a new age

2019 Fiscal Year Final Research Report

• Project/Area Number: 17K01272
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Social systems engineering/Safety system
• Research Institution: Tokyo University of Science
• Principal Investigator: Shi Jianming 東京理科大学, 経営学部ビジネスエコノミクス学科, 教授 (70287465)
• Project Period (FY): 2017-04-01 – 2020-03-31
• Keywords: 線形計画 / LP-Newton法 / 強多項式のアルゴリズム / 平面回転

Outline of Final Research Achievements

For solving a linear programming problem with box constraints, we designed the algorithm so that the "faces" corresponding to the vertices of the box constraint. This algorithm is able to find an optimal solution without using Wolfe's algorithm for finding the minimum norm on a Zonotope.
The algorithm in this study was compared with the LP-Newton method by numerical experiments. When the dimension is 1000 and the number of constraints is 150, the CPU time to find a optimal solution by LP-Newton method is 34.3 seconds and while it is 5.9 seconds by the proposed method. The number of using the Newton steps dropped from 4.0 to 2.0 on average. We believe that the proposed method was observed to be superior in terms of calculation speed.

Free Research Field

数理工学

Academic Significance and Societal Importance of the Research Achievements

LP 問題はある種の計算幾何学の問題に帰着でき,既存の変換よりさらに高速のアルゴリズムの開発を今後期待できる.本研究では, LP-Newton法の改良法の一例を示したが,今後も大きな改良を行われ,線形計画のさらなる発展につなげたい.
今まで以上にデータ分析を必要とする新時代に,かつてない高速なアルゴリズムは人工知能, 機械学習などの分野に広く利用され,大きな意義がある. また,線形計画問題に対する強多項式のアルゴリズムの開発に少しでも刺激を与えて, 多くの若い研究者が参入し,線形計画の分野に革新をもたらすて頂けると,データサイエンスや人工智能,数値計算などの周辺分野の発展に寄与することになる.