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On affine scaling algorithms for nonconvex quadratic programming. (English) Zbl 0767.90065
Summary: 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 converges to a feasible point satisfying both the first and the second order optimality conditions.

MSC:
90C26 Nonconvex programming, global optimization
90C20 Quadratic programming
90C60 Abstract computational complexity for mathematical programming problems
90-08 Computational methods for problems pertaining to operations research and mathematical programming
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