Optimization based on discrete structure representations

2022 Fiscal Year Final Research Report

• Project/Area Number: 19H04174
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Review Section: Basic Section 61030:Intelligent informatics-related
• Research Institution: Kyushu University
• Principal Investigator: Hatano KOhei 九州大学, 基幹教育院, 准教授 (60404026)
• Co-Investigator(Kenkyū-buntansha): 瀧本 英二 九州大学, システム情報科学研究院, 教授 (50236395)
• Project Period (FY): 2019-04-01 – 2022-03-31
• Keywords: 連続最適化 / 離散最適化 / 拡張定式化 / 決定ダイアグラム

Outline of Final Research Achievements

In this project, we propose a method to obtain a concise extended formulation of a given optimization problem with linear constraints of integer coefficients, based on the Non-deterministic ZDD (NZDD) representation of the linear constraits. Our method is applicable to wide classes of optimization problems such as LP, QP, SDP and MIP. Furthermore, we propose an extention of our method to the 1-norm regularized soft margin optimization problem,a standard formulation of learning sparse linaer classifiers. In the experiments on synthetic and real datasets, our method often improves compuation time and maximum memory usage compared to the naive application of optimization solvers.

Free Research Field

機械学習

Academic Significance and Societal Importance of the Research Achievements

オペレーションズ・リサーチや機械学習・人工知能分野において，大規模な最適化問題を解く必要性は高まっている．本手法は大規模な線形制約の冗長性を利用して，簡潔かつ等価な最適化問題に変換するものであり，基盤技術としてその潜在的な貢献は大きいといえる．