A Lagrange Newton Method with Inexact Jacobians for Large Scale Inequality Constrained Optimization

Description:  We present a Lagrange Newton method for solution of large scale nonlinear programs with equality and inequality constraints. To avoid an expensive evaluation of the complete constraint Jacobian we propose a novel approach that does not need exact constraint Jacobians. The method uses inexact Jacobian matrices but an exact Lagrange gradient vector, similar to well known ideas for equality constrained optimization. Here, the exact Lagrange gradient can efficiently be computed by techniques of the reverse mode of automatic differentiation at the computational cost of only five function evaluations. We show how these ideas can be extended to treat inequality constraints by a simple modification of existing Lagrange Newton, or sequential quadratic programming, methods. Our focus is less on how to obtain the inexact Jacobians -- they may be obtained by quasi-Newton updates or cheaply approximated otherwise -- but on the treatment of inequalities. We show and illustrate that the proposed inexact jacobian Lagrange Newton method is able to detect the correct active set in the presence of inexact inequality constraint jacobians. We also show linear local convergence under mild conditions once the active set is determined. Finally, we apply the method to optimal control problems that involve discretized instationary partial differential equations. Area(s): Date:  2004-07-20 Start Time:   14:30 Speaker:  Moritz Diehl, Interdisciplinary Center for Scientific Computing, University of Heidelberg Place:  Room 5.5 Research Groups: -Numerical Analysis and Optimization See more:   <Main>