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Inexact solution of auxiliary problems in Polyak type algorithms. (English) Zbl 0972.90052
Summary: The Polyak algorithm is known to be an efficient algorithm for the iterative solution of quadratic programming problems with inequality constraints, especially when applied to small problems or appropriately modified. It reduces the solution of the above problems to the conjugate gradient solution of a sequence of unconstrained minimization problems. The point of this note is to show that before reaching the solution of an auxiliary minimization problem, there is a feasible decrease direction that can be used in order to release some active constraints in such a way that the finite termination property of the original algorithm is preserved.

MSC:
90C20 Quadratic programming
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