Stability and Efficiency of the Positive Definite Quadratic Programming Algorithms
Awatif M .A .Elsiddieg
Awatif M. A. Elsiddieg, Department of Mathematical, Faculty of Science& Humanities Studies, Prince Sattam Bin Abdul-Aziz University, Kingdom of Saudi Arabia.
Manuscript received on March 06, 2017. | Revised Version Manuscript Received on March 15, 2017. | Manuscript published on March 20, 2017. | PP: 4-26 | Volume-4, Issue-5, March 2017. | Retrieval Number: E0719034517/2017©BEIESP
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© The Authors. Published By: Blue Eyes Intelligence Engineering & Sciences Publication (BEIESP). This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
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 method[20].
Keywords: KKT-conditions, QR factorization, active set methods, penalty and barrier functions, complementrity.