Novel Interior Point Algorithms for Solving Nonlinear Convex Optimization Problems

• Published in: Advances in Operations Research Vol. 2015; no. 2015; pp. 59 - 65
• Main Authors: Tahmasebzadeh, Sakineh, Malek, Alaeddin, Navidi, H. R.
• Format: Journal Article
• Language: English
• Published: Cairo, Egypt Hindawi Limiteds 01.01.2015; Hindawi Publishing Corporation; John Wiley & Sons, Inc
• Subjects: Algorithms; Analysis; Convex programming; Linear programming; Mathematical optimization; Methods; Operations research; Optimization; Simplex method; United States
• ISSN: 1687-9147; 1687-9155; 1687-9155
• DOI: 10.1155/2015/487271

This paper proposes three numerical algorithms based on Karmarkar’s interior point technique for solvingnonlinear convex programming problems subject to linear constraints. The first algorithm uses the Karmarkaridea and linearization of the objective function. The second and third algorithms are modification ofthe first algorithm using the Schrijver and Malek-Naseri approaches, respectively. These three novel schemesare tested against the algorithm of Kebiche-Keraghel-Yassine (KKY). It is shown that these three novel algorithmsare more efficient and converge to the correct optimal solution, while the KKY algorithm fails insome cases. Numerical results are given to illustrate the performance of the proposed algorithms.