Please use this identifier to cite or link to this item: http://hdl.handle.net/1813/6687
 Title: Computing a Trust Region Step for a Penalty Function Authors: Coleman, Thomas F.Hempel, Christian Keywords: computer sciencetechnical report Issue Date: Jul-1987 Publisher: Cornell University Citation: http://techreports.library.cornell.edu:8081/Dienst/UI/1.0/Display/cul.cs/TR87-847 Abstract: We consider the problem of minimizing a quadratic function subject to an ellipsoidal constraint when the matrix involved is the Hessian of a quadratic penalty function (i.e., a function of the form $p(x) = f(x) + \frac{1}{2\mu} c(x)^{T} c(x))$. Most applications of penalty functions require $p(x)$ to be minimized for values of $\mu$ decreasing to zero. In general, as $\mu$ tends to zero the nature of finite precision arithmetic causes a considerable loss of information about the null space of the constraint gradients when $\nabla^{2}p(x)$ is formed. This loss of information renders ordinary trust region Newton's methods unstable and degrades the accuracy of the solution to the trust region problem. The algorithm of More and Sorenson [1983] is modified so as to be more stable and less sensitive to the nature of finite precision arithmetic in this situation. Numerical experiments clearly demonstrate the stability of the proposed algorithm. URI: http://hdl.handle.net/1813/6687 Appears in Collections: Computer Science Technical Reports

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