Abstract
In this paper, we study a modification of the Celis-Dennis-Tapia trust-region subproblem, which is obtained by replacing thel 2-norm with a polyhedral norm. The polyhedral norm Celis-Dennis-Tapia (CDT) subproblem can be solved using a standard quadratic programming code.
We include computational results which compare the performance of the polyhedral-norm CDT trust-region algorithm with the performance of existing codes. The numerical results validate the effectiveness of the approach. These results show that there is not much loss of robustness or speed and suggest that the polyhedral-norm CDT algorithm may be a viable alternative. The topic merits further investigation.
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The first author was supported in part by the REDI foundation and State of Texas Award, Contract 1059 as Visiting Member of the Center for Research on Parallel Computation, Rice University, Houston, Texas, He thanks Rice University for the congenial scientific atmosphere provided. The second author was supported in part by the National Science Foundation, Cooperative Agreement CCR-88-09615, Air Force Office of Scientific Research Grant 89-0363, and Department of Energy Contract DEFG05-86-ER25017.
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El-Alem, M.M., Tapia, R.A. Numerical experience with a polyhedral-norm CDT trust-region algorithm. J Optim Theory Appl 85, 575–591 (1995). https://doi.org/10.1007/BF02193057
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DOI: https://doi.org/10.1007/BF02193057