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R. Baker Kearfott
Department of Mathematics
University of Southwestern Louisiana
U.S.L. Box 4-1010, Lafayette, LA 70504-1010 USA
email: rbk@louisiana.edu - Jianwei Dian
Department of Mathematics
University of Southwestern Louisiana
U.S.L. Box 4-1010, Lafayette, LA 70504-1010 USA
email: jxd6152@louisiana.edu
It is of interest in various contexts to find approximate feasible points to problems that have equality, inequality and bound constraints. For example, in exhaustive search algorithms for global optimization, it is of interest to construct bounds around approximate feasible points, within which a true feasible point is proven to exist. In such exhaustive search algorithms, the approximate feasible point procedure can repeat a large number of times. So, it's of interest to have a good algorithm that can compute approximate feasible points quickly. Random search has been suggested. But we will show with both theoretical analysis and test results that more is needed. We have developed and tested a technique of computing approximate feasible points, which combines random search with a generalized Newton method for underdetermined systems. The test results indicate that this technique works well.
keywords: constrained optimization, underdetermined systems, generalized inverse, feasibility
For a TeX DVI file of this entire paper, see http://interval.louisiana.edu/GlobSol/Dian-approximate-optimizer.dvi.
For a Postscript copy, see http://interval.louisiana.edu/GlobSol/Dian-approximate-optimizer.ps.