On constrained optimization by adjoint based quasi-Newton methods

Abstract:

In this article we propose a new approach to constrained optimization that is based on direct and adjoint vector-function evaluations in combination with secant updating. The main goal is the avoidance of constraint Jacobian evaluations and the reduction of the linear algebra cost per iteration to O(n + m)2 operations in the dense, unstructured case. A crucial building block is a transformation invariant two-sided-rank-one update (TR1) for approximations to the (active) constraint Jacobian. In this article we elaborate its basic properties and report preliminary numerical results for the new total quasi-Newton approach on some small equality constrained problems. A nullspace implementation under development is briefly described. The tasks of identifying active constraints, safeguarding convergence and many other important issues in constrained optimization are not addressed in detail.

Año de publicación:

2002

Keywords:

• KKT system
• Quasi-Newton
• Constrained optimization
• Lagrangian gradient
• Secant updating

Fuente:

scopus