| Budget Amount *help |
¥5,330,000 (Direct Cost: ¥4,100,000、Indirect Cost: ¥1,230,000)
Fiscal Year 2014: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2013: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2012: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| 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.
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