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)

Since 1984 there has been a concentrated e ort to develop e cient interior-point methods for linear programming (LP). In the last few years researchers have begun to appreciate a very important property of these interior-point methods (beyond their e ciency for LP): they extend gracefully to nonlinear convex optimization problems. New interior-point algorithms for problem classes such as semide nite programming (SDP) or second-order cone programming (SOCP) are now approaching the extreme e ciency of modern linear programming codes. In this paper we discuss three examples of areas of control where our ability to e ciently solve nonlinear convex optimization problems opens up new applications. In the rst example we show how SOCP can be used to solve robust open-loop optimal control problems. In the second example, we show how SOCP can be used to simultaneously design the set-point and feedback gains for a controller, and compare this method with the more standard approach. Our nal application concerns analysis and synthesis via linear matrix inequalities and SDP. Submitted to a special issue of Journal of Process Control, edited by Y. Arkun & S. Shah, for papers presented at the 1997 IFAC Conference onAdvanced Process Control, June 1997, Ban. This and related papers available via anonymous FTP at