Abstract
We investigate the use of interior algorithms, especially the affine-scaling algorithm, to solve nonconvex — indefinite or negative definite — quadratic programming (QP) problems. Although the nonconvex QP with a polytope constraint is a “hard” problem, we show that the problem with an ellipsoidal constraint is “easy”. When the “hard” QP is solved by successively solving the “easy” QP, the sequence of points monotonically converge to a feasible point satisfying both the first and the second order optimality conditions.
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Research supported in part by NSF Grant DDM-8922636 and the College Summer Grant, College of Business Administration, The University of Iowa.
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Ye, Y. On affine scaling algorithms for nonconvex quadratic programming. Mathematical Programming 56, 285–300 (1992). https://doi.org/10.1007/BF01580903
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DOI: https://doi.org/10.1007/BF01580903