Matrix Optimization Algorithms
by
Mohan C. Joshi
Industrial Mathematics Group, Department of Mathematics, Indian Institute of Technology Bombay, Powai, Mumbai - 400076, India
Coauthors: Ramaprasad. M.K.

A class of optimization algorithms called ``Matrix Optimization Algorithms''(MOA), is developed. The problems are classified into two categories - unconstrained and constrained. In the constrained category we deal with two types of problems, discrete and continuous. In the discrete type the objective function is optimized with respect to a matrix which appears in the equation of constraints. And in the continuous type, we deal with optimization problems where the constraint equation is given by a dynamical system. Our algorithms are based on the methods of steepest descent and conjugate gradient. As a corollary we obtain training algorithm for an artificial neural network, which is similar to feed forward neural network. We follow up by concrete applications to heat treatment analysis of ball bearings and solvability of matrix equations.

Date received: March 27, 2003