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An algorithm for convex quadratic programming that requires $O\left({n}^{3,5}L\right)$ arithmetic operations. (English) Zbl 0714.90075

S. Kapoor and 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.

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.

The paper gives complete references and informations, is very clearly written, and has many interesting applications.

Reviewer: A.Donescu
##### MSC:
 90C20 Quadratic programming 90C25 Convex programming 90C60 Abstract computational complexity for mathematical programming problems