A Quadratically Convergent Lagrangian Algorithm for Nonlinear Constraints
|An algorithm for the nonlinearly constrained optimization problem is presented. The algorithm consists of a sequence of major iterations generated by linearizing each nonlinear constraint about the current point, and adding to the objective function a linear penalty for each nonlinear constraint. The resulting function is essentially the Lagrangian. A Kantorovich-type theorem is given, showing quadratic convergence in terms of major iterations. This theorem insures quadratic convergence if the starting point (or any subsequent point) satisfies a condition which can be tested using computable bounds on the objective and constraint functions.
|University of Wisconsin-Madison Department of Computer Sciences
|A Quadratically Convergent Lagrangian Algorithm for Nonlinear Constraints
Files in this item
This item appears in the following Collection(s)
CS Technical Reports
Technical Reports Archive for the Department of Computer Sciences at the University of Wisconsin-Madison