Development of Approximation Algorithms with Theoretical Guarantee for Integer Programming Problem with Nonlinear Constraint

2015 Fiscal Year Final Research Report

• Project/Area Number: 24500002
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Fundamental theory of informatics
• Research Institution: Tokyo Institute of Technology (2015); Tohoku University (2012-2014)
• Principal Investigator: Shioura Akiyoshi 東京工業大学, 社会理工学研究科, 准教授 (10296882)
• Project Period (FY): 2012-04-01 – 2016-03-31
• Keywords: 整数計画問題 / 非線形関数 / アルゴリズム / 離散最適化 / 離散凸解析

Outline of Final Research Achievements

In this research, we consider integer programming problems with nonlinear objective functions and nonlinear inequality constraints, and aimed at developing approximation algorithms with theoretical guarantee for quality of solutions and running times. As the main results of this research, we proposed an approximation algorithm for the maximization of M-concave function with multiple knapsack constraints, and showed that the proposed algorithm finds an approximate solution that is arbitrarily close to an optimal solution in polynomial time. The proposed algorithm is developed based on a continuous relaxation approach. We also consider the maximization of the sum of two M-concave functions, and showed that an approximate solution that is arbitrarily close to an optimal solution can be obtained in polynomial time by using a Lagrangian relaxation approach.

Free Research Field

離散最適化