Analytical Study on Vector Optimization and its Applications into Mathematical Programming Problems

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In this research, we have studied several kinds of themes on vector optimization analytically and broadly and then we got some results on saddle point's existence, vector equilibrium problem, convexity and semicontinuity for set-valued maps under systematic research and investigation. Moreover, we have studied on efficient solutions of multicriteria location problems. The main results and presentations are as follows.1.We presented our results on characterization of efficient solutions and existence of cone saddle points at The Second and Third International Conferences on Nonlinear Analysis and Convex Analysis(NACA2001,NACA2003), held at Hirosaki University and Tokyo Institute of Technology, August 2001 and August 2003, respectively. We delivered invited talks on multicriteria minimax inequality which is fundamental for cone saddle point of vector-valued function at NACA2003 and Workshop on Nonlinear Analysis & Convex Analysis, November 2003. Moreover, we organized the Fifth International Conference on Multi-Objective Programming and Goal Programming : Theory & Applications(MOPGP'02) at Nara, June 2002, and we discussed several problems and topics in this meeting.2.We presented our results on several inherited properties of scalarizing functions from convexity and semicontinuity of set-valued maps at NACA2001, MOPGP'02, and NACA2003. These results were presented in RIMS Symposium on Nonlinear Analysis and Convex Analysis.3.We presented our results on multicriteria game at NACA2001,MOPGP'02, and NACA2003.4.We presented our results on multicriteria location problems at NACA2001 and NACA2003. These results were presented in RIMS Symposium on Nonlinear Analysis and Convex Analysis. We also presented them at the research group of "decision and OR" of the Operations Research Society of Japan, held at Fukui University of Technology.