Parallel Filter Trust Region Algorithm for Partially Separable Problems

We propose a parallelization of the multidimensional filter trust region methods to make them suitable for large scale problems. The parallelization reduces the storage problems caused by storing the filter point. The limited memory BFGS method is employed to obtain the Hessian approximation in the quadratic model of the trust region methods, which often yields a dramatic reduction in the number of function and gradient evaluation. As the special structure of the partially separable functions, each processor has to solve the subproblem in a lower dimensional subspace. Numerical results show that the parallelization is efficient.