Abstract
In this paper we introduce some stable and efficiency algorithms for the positive definite quadratic programming . Sections (1), introduce matrix factorizations QR factorization ,orthogonal transformation using Householder matrices , which leads to our main work. In section(2) general consideration is given. In section (3) we introduce the basic concepts methods linear equality and inequality constraints that leads to our methods. In section (4) we give some of the stable and efficiency algorithms for positive quadratic programming only using KKT-conditions. We conclude our paper by showing that there are stable and efficient methods for indefinite programming as the extended Dantzig Wolfe method20.
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