This paper is concerned with the numerical solution of a Karush–Kuhn–Tucker system. Such symmetric indefinite system arises when we solve a nonlinear programming problem by an Interior-Point (IP) approach. In this framework, we discuss the effectiveness of two inner iterative solvers: the method of multipliers and the preconditioned conjugate gradient method. We discuss the implementation details of these algorithms in an IP scheme and we report the results of a numerical comparison on a set of large scale test-problems arising from the discretization of elliptic control problems.
Some iterative methods for the solution of a symmetric indefinite KKT system / Bonettini, S.; Ruggiero, V.. - In: COMPUTATIONAL OPTIMIZATION AND APPLICATIONS. - ISSN 0926-6003. - 38:1(2007), pp. 3-25. [10.1007/s10589-007-9039-7]
Some iterative methods for the solution of a symmetric indefinite KKT system
Bonettini S.
;
2007
Abstract
This paper is concerned with the numerical solution of a Karush–Kuhn–Tucker system. Such symmetric indefinite system arises when we solve a nonlinear programming problem by an Interior-Point (IP) approach. In this framework, we discuss the effectiveness of two inner iterative solvers: the method of multipliers and the preconditioned conjugate gradient method. We discuss the implementation details of these algorithms in an IP scheme and we report the results of a numerical comparison on a set of large scale test-problems arising from the discretization of elliptic control problems.
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