A Quadratically Convergent Lagrangian Algorithm for Nonlinear Constraints
University of Wisconsin-Madison Department of Computer Sciences
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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.