Coordinator：

Soon Yi Wu (NCKU)

Optimization, Functional Analysis, Linear Programming

soonyi@mail.ncku.edu.tw

Tel: +886-6-2757575 Ext. 65133

 

Background, Current Status, and Modes of Operation ：

Section A. Optimization and Numerical Computation

Optimization and numerical computation is understood in a board sense, including mathematical programming, computational optimization, operational research, and global optimization. Currently there are over 10 active number researchers in Taiwan . Research topics include: infinite and semi-infinite programming, generalized variational inequality and duality, fractional programming, nonlinear programming, and control. A regular optimization and numerical computation seminar is run at NCTS biweekly, including talks given by foreign visitors and reports on research results given by members of the local focus group. Also, there are some optimization seminars at NSYSU, with invited foreign visitors joining from time to time.

 

Main research focus of optimization and numerical computation group at the subproject II of NCTS

  1. Infinite and semi-infinite programming
  2. Vector variational inequality
  3. Vector optimization
  4. Fractional programming
  5. Non-convex global optimization
  6. Optimal Control

Student Seminars and Schools

We held student-seminars once a week for graduate students in optimization and numerical computation. We also plan to open summer school or winter school for graduate students and advanced undergraduates interested in optimization and numerical computation. The participating students would be guided by professors from the focus group and some visiting professor from foreign countries. NCTS would also offer partial financial support for Ph.D. students participate in the conferences or workshops held abroad.

 

Section B. Partial Differential Equation

PDE group is one of the largest mathematical communities in the world and in Taiwan as well. The subgroup associated with Tainan office has many active mathematicians senior or junior and they have made substantial progress in research and education which can not happen without the support of NCTS. To maintain and even enhance the activity of PDE subgroup of Tainan and the well-establishment of junior mathematicians in the future, it is vital for our subgroup continuously to receive the support from NCTS.

 

In recent years, the Tainan subgroup has been active in the following researching subject: inverse problems, eigenvalue problems, traveling waves, semilinear elliptic equations, Homogenization, biomathematics, Dirac-Klein-Gordon equations, and Schrödinger equation. Many good quality papers were published every year. Seminars with local or foreign speakers have been arranged on regular base. We also have students' seminars on important and interesting topics of PDEs for educational purpose. We will enhance the current modes of operations in the new proposal and manage the resources in an efficient way to achieve more in both research and education.

 

Focus of NCTS at Tainan

  1. Cauchy problem for nonlinear wave equations
  2. Scattering Problems
  3. Quantitative unique continuation
  4. Homogenization Problems for Partial Differential Equations
  5. Inverse Problems and eigenvalue Problems
  6. Nonlinear Schrödinger Systems with trap Potentials
  7. Similarity solution in boundary layer theory
  8. Wave propagations in the multi-dimensional domain