### Optimization and Systems Theory Seminar

Monday, June 16, 2003, 11.00-12.00, Room 3721, Lindstedtsv. 25

**Michael Friedlander**

Mathematics and Computer Science Division (MCS)

Argonne National Laboratory

Argonne, IL 60439

USA

E-mail: michael@mcs.anl.gov

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An LCL algorithm for constrained optimization

For optimization problems with nonlinear constraints, linearly
constrained Lagrangian (LCL) methods sequentially minimize an
augmented Lagrangian subject to linearized constraints.
Convergence is rapid near a solution (as proved by Robinson and
often observed with MINOS).
To induce global convergence and to unify the approaches used
in LANCELOT and MINOS, we work with an elastic form of the
linearized constraints (by adding an L1 penalty term to the
augmented Lagrangian). Our stabilized LCL method possesses
two important properties: the linearly constrained subproblems
are always feasible, and they may be solved inexactly.

The current implementation is efficient on large problems, using
MINOS to solve the subproblems. Only first derivatives are
required. We present numerical results on the COPS and CUTE
test problems.

Calendar of seminars

*Last update: June 5, 2003 by
Anders Forsgren,
anders.forsgren@math.kth.se.
*