A trust region and affine scaling interior point method for nonconvex minimization with linear inequality constraints |
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Authors: | Thomas F Coleman Yuying Li |
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Institution: | (1) Cornell University, Comp. Sc. Dept. and Ctr. Appl. Math., 647 Rhodes Hall, Ithaca, NY 14853, USA, e-mail: coleman@tc.cornell.edu, US;(2) Computer Science Dept., Cornell University, USA, US |
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Abstract: | A trust region and affine scaling interior point method (TRAM) is proposed for a general nonlinear minimization with linear
inequality constraints 8]. In the proposed approach, a Newton step is derived from the complementarity conditions. Based
on this Newton step, a trust region subproblem is formed, and the original objective function is monotonically decreased.
Explicit sufficient decrease conditions are proposed for satisfying the first order and second order necessary conditions.?The
objective of this paper is to establish global and local convergence properties of the proposed trust region and affine scaling
interior point method. It is shown that the proposed explicit decrease conditions are sufficient for satisfy complementarity,
dual feasibility and second order necessary conditions respectively. It is also established that a trust region solution is
asymptotically in the interior of the proposed trust region subproblem and a properly damped trust region step can achieve
quadratic convergence.
Received: January 29, 1999 / Accepted: November 22, 1999?Published online February 23, 2000 |
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Keywords: | : trust region – interior point method – Dikin-affine scaling – Newton step |
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