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Zbl 0714.90075
Mehrotra, Sanjay; Sun, Jie
An algorithm for convex quadratic programming that requires $O(n\sp{3,5}L)$ arithmetic operations.
(English)
[J] Math. Oper. Res. 15, No.2, 342-363 (1990). ISSN 1526-5471; ISSN 0364-765X/e

{\it S. Kapoor} and {\it P. M. Vaidya} [Proc. 18th Annual ACM Sympos. Theory of Computing, 147-159 (1985)] proposed an algorithm for solving quadratic programs, based upon Karmarkar's ideas of solving linear programs. After Kapoor and Vaidya several authors have recently proposed new algorithms for improving the worst case bound for solving quadratic programs. The common idea of all these algorithms is that they explicitly maintain primal and dual feasibility. \par In this paper the authors propose an algorithm for the solution of quadratic programs that does not depend on duality analysis. They build a sequence of nested convex sets that shrink towards the set of optimal solutions. During iteration k they take a partial Newton step to move from an approximate analytic center to another one. \par The paper gives complete references and informations, is very clearly written, and has many interesting applications.
[A.Donescu]
MSC 2000:
90C25 Convex programming
90C60 Abstract computational complexity for math. programming problems

Keywords: convex quadratic programming; interior point methods; Karmarkar's algorithm; worst case bound; sequence of nested convex sets; approximate analytic center

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