A Quadratically Convergent Lagrangian Algorithm for Nonlinear Constraints
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- Author(s)
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Rosen, J.B.; Kreuser, J.L.
- Publisher
- University of Wisconsin-Madison Department of Computer Sciences
- Date
- Mar 15, 2012
- Abstract
- 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.
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http://digital.library.wisc.edu/1793/57778
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