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The research described in this report deals with the development of (1) efficient, consistent discretization techniques for use in semi-infinite optimization, optimal control algorithms that solve problems with dynamics governed by partial differential equations, (2) superlinearly converging semi- finite optimization algorithms, (3) various techniques for finding design parameters satisfying specifications, (4) optimal control algorithms for discrete and distributed systems with control, state and shape constraints, and (5) efficient numerical procedures for the integrated design of flexible structures and their control systems.... Optimization, Optimal shape design algorithms.