ELEMENT-BY-ELEMENT PRECONDITIONERS FOR LARGE PARTIALLY SEPARABLE OPTIMIZATION PROBLEMS

We study the solution of large-scale nonlinear optimization problems b y methods which aim to exploit their inherent structure. In particular , are consider the property of partial separability, first studied by Griewank and Toint [Nonlinear Optimization, 1981, pp. 301-312]. A typi cal minimization method for nonlinear optimization problems approximat ely solves a sequence of simplified linearized subproblems. In this pa per, we explore how partial separability may be exploited by iterative methods for solving these subproblems. We particularly address the is sue of computing effective preconditioners for such iterative methods. We concentrate on element-by-element preconditioners which reflect th e structure of the problem. We find that the performance of these meth ods can be considerably improved by amalgamating elements before apply ing the preconditioners. We report the results of numerical experiment s which demonstrate the effectiveness of this approach.