Abstract
We consider a quadratic program equivalent to the general problem of minimizing a convex quadratic function of many variables subject to linear inequality constraints.
In previous work [12], one of us presented an algorithm related to such problems, and classified them under “combinatorial equivalence”. The classification contained linear programs at one end (where the function has zero quadratic part) and least-distance programs at the other. A least-distance program is a problem of finding a point of a convex polyhedron which is at least distance from a given point; such programs have been studied by one of us [15, 17] and were shown to correspond to that case of the general problem where the function has positive definite quadratic part.
We now extend the work on least-distance programs to those programs intermediate between linear and least-distance (called “essentially bisymmetric” in [12]), and show that such programs are really “hybrids”, with traits inherited from both parent programs: linear and leastdistance.
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This work was supported in part by Office of Naval Research Contract No. N00014-67-A-0151-0010 (Princeton University).
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Parsons, T.D., Tucker, A.W. Hybrid programs: Linear and least-distance. Mathematical Programming 1, 153–167 (1971). https://doi.org/10.1007/BF01584084
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DOI: https://doi.org/10.1007/BF01584084