A Semidefinite Program (SDP) is a fundamental problem in mathematical programming. It is a large scheme which includes linear programs, second-order cone programs and semidefinite programs. It has many applications covering various fields such as combinatorial optimization, systems and control theory, robust optimization and quantum chemistry. Primal-dual interior-point methods, which are polynomial-time algorithms, were proposed to solve semidefinite programs. SDPA is based on the primal-dual interior-point method. In addition, SDPA utilizes sparsity of data in several ways and parallel computation to solve huge size problems efficiently.
In my laboratory, we focus our research mainly on Operations Research and Data Mining. Due to the recent improvements on the computer hardware and the efficiency of optimization algorithms, it has been possible to analyse large-scale mathematical models nowadays. However, there is a continuous desire for obtaining more precise analysis of these models. To achieve this, our laboratory proposal is to develop innovative optimization algorithm and their implementations as a software. I want that students of my laboratory could acquire potentials to create an abstract and a logical representations of problems through a mathematical training. I also want to prepare students who master computational mathematics by understanding fundamental principles of its functionality.