Our laboratory researches the theory and application of mathematical optimization. It is one of the leading methodologies for using mathematical systems approaches to solve a wide range of issues arising in real social settings. Application fields of optimization are too many to enumerate and it is virtually certain that these fields will expand in both breadth and importance in the coming years. In our laboratory, the basic guideline is to conduct research that is oriented towards theory but has a firm grasp of applications to real-world problems.
We examine a wide range of problems and techniques, some of which are listed below.
1. Development of new algorithms for basic, important mathematical programming problems, such as linear programming problems, convex programming problems, nonlinear programming problems, network programming problems, combinatorial programming problems, complementarity problems, variational inequality problems, multiobjective programming problems, etc. We endeavor to provide theoretical descriptions of their nature and to use computational experiments to verify their utility.
2. Research into stochastic optimization and robust optimization, which plays an important role in risk-aware decision-making, and development of new techniques for equilibrium problems and mathematical programs with equilibrium constraints (MPEC) arising in fields such as engineering science and social science.
3. Modeling of optimization problems in traffic engineering, financial engineering, data mining, communication engineering, and game theory, as well as development of efficient computational algorithms.