An Hybrid Interior Point Algorithm for Performing Alternating Minimizations an Hybrid Interior Point Algorithm for Performing Alternating Minimizations

Optimization using alternating minimization (AM) alternately minimizes an objective function with respect to two disjoint subsets of a function's parameters. AM algorithms are useful for optimization problems which can be decomposed into convex subproblems. AM algorithms have recently appeared in the neural computing community. This paper examines the use of recently developed Interior Point (IP) techniques to implement an AM algorithm which solves an important class of optimization problems. The IP techniques studied in this paper solve optimization problems that can be decomposed into linear and quadratic subproblems. Such problems appear frequently in multiple model parameter identiication. The proposed algorithm is a version of the generalized Expectation-Maximization algorithm and is proven to converge to locally optimal solutions in O(p nL) iterations with an associated computational cost of max(O(n 3:5 L); O(n 1:5 R 2 L); O(p nM R 3 L)) where n is the dimension of an associated linear programming problem, M is the number of models, R is the dimension of the parameter vectors being identiied, and L is a measure of the solution's accuracy.