A method for multi-dimensional nonlinear knapsack problems and its application 多次元非線形ナップザック問題の解法とその応用

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Title: A method for multi-dimensional nonlinear knapsack problems and its application

博士論文

Contents / p1 (0004.jp2)
1 INTRODUCTION / p3 (0005.jp2)
1.1 Brief Review / p3 (0005.jp2)
1.2 Summary of Contents / p4 (0006.jp2)
2 FORMULATION OF PROBLEMS / p7 (0007.jp2)
2.1 Multi-Dimensional Nonlinear Knapsack Problem / p7 (0007.jp2)
2.2 Surrogate Constraints Method / p9 (0008.jp2)
2.3 Concluding Remarks / p10 (0009.jp2)
3 ALGORITHMS FOR SURROGATE DUAL PROBLEM / p13 (0010.jp2)
3.1 Modular Approach (MA) / p13 (0010.jp2)
3.2 Cut-Off Polyhedron Algorithm (COP) / p16 (0012.jp2)
3.3 Computational Experiments / p18 (0013.jp2)
3.4 Concluding Remarks / p18 (0013.jp2)
4 AN APPROXIMATE METHOD / p21 (0014.jp2)
4.1 Brief Review of Approximate Method / p21 (0014.jp2)
4.2 Reduction of Feasible Region of Surrogate Problem / p22 (0015.jp2)
4.3 Computational Experiments / p24 (0016.jp2)
4.4 Concluding Remarks / p27 (0017.jp2)
5 APPLICATION TO NONLINEAR INTEGER PROGRAMMING PROBLEMS / p29 (0018.jp2)
5.1 Formulation of Problems / p29 (0018.jp2)
5.2 Computational Experiments / p30 (0019.jp2)
5.3 Concluding Remarks / p35 (0021.jp2)
6 APPLICATION TO NONLINEAR PROGRAMMING PROBLEMS / p37 (0022.jp2)
6.1 Formulation of Problems / p37 (0022.jp2)
6.2 One-Dimensional Problems / p39 (0023.jp2)
6.3 Multi-Dimensional Problems / p44 (0026.jp2)
6.4 Concluding Remarks / p46 (0027.jp2)
7 CONCLUSION / p51 (0029.jp2)
REFERENCES / p53 (0030.jp2)
ACKNOWLEDGMENT / p57 (0032.jp2)

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