Fast Algorithms for Large Scale Convex Optimization Involving Linear Matrix Inequality

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9411664 Fan With recent dramatic increase in available computing power, numerical optimization has become an attractive tool for analysis and design of complex systems. There are a large number of problems in science and engineering which can be formulated as convex optimization problems involving linear matrix inequality. This problem is inherently difficult to solve as the nonsmoothness usually occurs at the solution. Further, as systems are becoming more complex, the resulting optimization problems tend to have a large number of decision variables as well as constraints. Therefore, several basic computation components such as inversion of a matrix, eigenvalue and eigenvector calculation, or evaluation of the Hessian matrix, that needed for most methods become either prohibited or very costly to perform. It is then necessary to use approximations and yet have the fast rate of convergence preserved. ***