Detecting Infeasibility in Infeasible-Interior-Point Methods for Optimization
نویسنده
چکیده
We study interior-point methods for optimization problems in the case of infeasibility or unboundedness. While many such methods are designed to search for optimal solutions even when they do not exist, we show that they can be viewed as implicitly searching for well-defined optimal solutions to related problems whose optimal solutions give certificates of infeasibility for the original problem or its dual. Our main development is in the context of linear programming, but we also discuss extensions to more general convex programming problems. ∗School of Operations Research and Industrial Engineering, Cornell University, Ithaca, New York 14853, USA ([email protected]). This author was supported in part by NSF through grant DMS-0209457 and ONR through grant N00014-02-1-0057.
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