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 toward theory but has a firm grasp of applications to real-world problems.
We examine many problems and techniques, some of which are listed below.
1. Development of new algorithms for basic, important mathematical optimization problems, such as linear optimization problems, convex optimization problems, nonlinear optimization problems, network optimization problems, semidefinite optimization problems, conic optimization problems, multi-objective optimization problems, complementarity problems, variational inequality 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 the 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, machine learning (artificial intelligence), wireless communications, and game theory, as well as development of efficient computational algorithms.