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During the contract period we made considerable progress, developing new families of convex optimization problems for use in control engineering, forging new areas of control applications, and improvements in algorithms. Two new families of convex optimization problems studied are determinant maximization with LMI constraints, and second order cone programming. Interior point code has been developed and tested for both of these, that are already widely used and cited. We have also developed a preliminary second (sparse) version of our original semidefinite programming code SP, and new sophisticated methods of global optimization used for nonconvex programming have been successfully extended to the BMI problem. We have pursued a number of applications including a new method for FIR filter design using spectral factorization and convex optimization, robust open loop model predictive control using second order programming, VLSI circuit synthesis via semidefinite programming, and low authority control via convex optimization. Previous work on developing fast algorithms for carrier phase GPS has also continued and the methods have been applied with success to spacecraft formation flying.