Hierarchically structured unit-simplex transformations for parallel distributed optimization problems

A stable deterministic approach is presented for incorporating unit-simplex constraints based on a hierarchical deformable-template structure. This approach (i) guarantees strict confinement of the search to the unit-simplex constraint set without introducing unwanted constraints; (ii) leads to a hierarchical, rather than a global, network interconnection structure; (iii) allows multiresolution processing; and (iv) allows easy closed-form incorporation of certain other inherently global constraints, such as general recursive symmetries. Selected examples are presented which illustrate and demonstrate large-scale application of the template method