The Implementation of the Primal-Dual Interior-Point Method for the Semidefinite Programs and its Engineering Applications

In resent years, semidefinite program (SDP) has been intensively studies both in theoretical and practical aspects of various fields including interior-point method, combinatorial optimization and the control and systems theory. The SDPA (SemiDefinite Programming Algorithm) [4] is a C++ implementation of a Mehrotra-type primal-dual predictor-corrector interior-point method for solving the standard form semidefinite program. The SDPA incorporates data structures for handling sparse matrices and an efficient method proposed by Fujisawa et al. [5] for computing search directions when problems to be solved are large scale and sparse. Finally, we report numerical experiments of the SDP for the structural optimization under multiple eigenvalue constraints.