Single and dual wavelength exposure of photoresist
J. LaRue, C. Ting
Proceedings of SPIE 1989
We present and analyze an interior-exterior augmented Lagrangian method for solving constrained optimization problems with both inequality and equality constraints. This method, the modified barrier-augmented Lagrangian (MBAL) method, is a combination of the modified barrier and the augmented Lagrangian methods. It is based on the MBAL function, which treats inequality constraints with a modified barrier term and equalities with an augmented Lagrangian term. The MBAL method alternatively minimizes the MBAL function in the primal space and updates the Lagrange multipliers. For a large enough fixed barrier-penalty parameter the MBAL method is shown to converge Q-linearly under the standard second-order optimality conditions. Q-superlinear convergence can be achieved by increasing the barrier-penalty parameter after each Lagrange multiplier update. We consider a dual problem that is based on the MBAL function. We prove a basic duality theorem for it and show that it has several important properties that fail to hold for the dual based on the classical Lagrangian.
J. LaRue, C. Ting
Proceedings of SPIE 1989
Satoshi Hada
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Charles A Micchelli
Journal of Approximation Theory
Fausto Bernardini, Holly Rushmeier
Proceedings of SPIE - The International Society for Optical Engineering