A finite step projective algorithm for solving linear matrix inequalities

This paper presents an algorithm for finding feasible solutions of linear matrix inequalities. The algorithm is based on the method of alternating projections (MAP), a classical method for solving convex feasibility problems. Unlike MAP, which is an iterative method that converges asymptotically to a feasible point, the algorithm converges after a finite number of steps. The key computational component of the algorithm is an eigenvalue-eigenvector decomposition which is carried out at each iteration. Computational results for the algorithm are presented and comparisons are made with existing algorithms.