this paper is organized as follows. First, we discuss the formulation of the semidefinite programming problem used by CSDP. We then describe the predictor corrector algorithm used by CSDP to solve the SDP. We discuss the storage requirements of the algorithm as well as its computational complexity. Finally, we present results from the solution of a number of test problems. 2 The SDP Problem We consider semidefinite programming problems of the form max tr (CX)

A wide variety of nonlinear convex optimization problems can be cast as problems involving linear matrix inequalities (LMIs), and hence e ciently solved using recently developed interior-point methods. In this paper, we will consider two classes of optimization problems with LMI constraints: The semide nite programming problem, i.e., the problem of minimizing a linear function subject to a linear matrix inequality. Semide nite programming is an important numerical tool for analysis and synthesis in systems and control theory. It has also been recognized in combinatorial optimization as a valuable technique for obtaining bounds on the solution of NP-hard problems. The problem of maximizing the determinant of a positive de nite matrix subject to linear matrix inequalities. This problem has applications in computational geometry, experiment design, information and communication theory, and other elds. We review some of these applications, including some interesting applications that are less well known and arise in statistics, optimal experiment design and VLSI. 1 Optimization problems involving LMI constraints We consider convex optimization problems with linear matrix inequality (LMI) constraints, i.e., constraints of the form F (x) =F0+x1F1+ +xmFm 0; (1) where the matrices Fi = F T i 2 R n n are given, and the inequality F (x) 0 means F (x) is positive semide nite. The LMI (1) is a convex constraint in the variable x 2 R m. Conversely, a wide variety of nonlinear convex constraints can be expressed as LMIs (see the recent