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1 Optimization under Linear Inequality Constraints |
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Authors: | TJ Smith |
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Institution: | (1) Department of Educational Technology, Research and Assessment, Northern Illinois University, |
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Abstract: | 1 optimization under linear inequality constraints based upon iteratively reweighted iterative projection (or IRIP). IRIP is
compared to a linear programming (LP) strategy for L1 minimization (Sp?th 1987, Chapter 5.3) using the ultrametric condition as an exemlar class of constraints to be fitted. Coded
for general constraints, the LP approach proves to be faster. Both methods, however, suffer from a serious limitation in being
unable to process reasonably-sized data sets because of storage requirements for the constraints. When the simplicity of vector
projections is used to allow IRIP to be coded for specific (in this case, ultrametric) constraints, we obtain a fast and efficient
algorithm capable of handling large data sets. It is also possible to extend IRIP to operate as a heuristic search strategy
that simultaneously identifies both a reasonable set of constraints to impose and the optimally-estimated parameters satisfying these constraints. A few noteworthy characteristics of L1 optimal ultrametrics are discussed, including other strategies for reformulating the ultrametric optimization problem. |
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