This study addresses both classical and previously unsolved optimization tasks in linear algebra, linear systems theory, control theory and signal processing. Exploiting developments in Computation such as Parallel Computing and Neural Networks, it gives a dynamical systems approach for tackling a wide class of constrained optimization tasks. Optimization and Dynamical Systems will be of interest to engineers and mathematicians. Engineers will learn the mathematics and the technical approach necessary to solve a wide class of constrained optimization tasks. Mathematicians will see how techniques from global analysis and differential geometry can be developed to achieve useful construction procedures for optimization on manifolds.