Matrices with lexicographically-ordered rows
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The lexicographic order can be used to force a collection of decision vectors to be all different, i.e., to take on different values in some coordinates. We consider the set of fixed-size matrices with bounded integer entries and rows in lexicographic order. We present a dynamic program to optimize a linear function over this set, from which we obtain a compact extended formulation for its convex hull.
KeywordsLexicographic order Extended formulation Dynamic programming
The author thanks an anonymous referee whose comments and suggestions greatly helped to improve the paper.