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A Novel Solution Approach using Linearization Technique for Nonlinear Programming Problems
| International Journal of Computer Applications |
| Foundation of Computer Science (FCS), NY, USA |
| Volume 181 - Number 12 |
| Year of Publication: 2018 |
| Authors: Mustafa Sivri, Inci Albayrak, Gizem Temelcan |
10.5120/ijca2018917703
|
Mustafa Sivri, Inci Albayrak, Gizem Temelcan . A Novel Solution Approach using Linearization Technique for Nonlinear Programming Problems. International Journal of Computer Applications. 181, 12 ( Aug 2018), 1-5. DOI=10.5120/ijca2018917703
Abstract
In this paper, a novel solution approach for solving the nonlinear programming (NLP) problems having m nonlinear algebraic inequality (equality or mixed) constraints with a nonlinear algebraic objective function in n variables using linearization technique is presented. This approach performs successive increments to find a solution of the NLP problem, based on the optimal solutions of linear programming (LP) problems, satisfying the nonlinear constraints oversensitively. In the proposed approach, the original problem is converted to the LP problem using increments in the linearization process and the impact of computational efficiency makes the performance of the solution well. It is presented that how the solution approach can be applied to solve the illustrated examples from the literature.
References
- Inci Albayrak, Mustafa Sivri, and Gizem Temelcan. A new iterative approach for solving nonlinear programming problem. New Trends in Mathematical Sciences, 6(2):68–77, 2018.
- H Basirzadeh, AV Kamyad, and S Effati. An approach for solving nonlinear programming problems. Korean Journal of Computational & Applied Mathematics, 9(2):547–560, 2002.
- Richard H Byrd, Nicholas IM Gould, Jorge Nocedal, and Richard A Waltz. An algorithm for nonlinear optimization using linear programming and equality constrained subproblems. Mathematical Programming, 100(1):27–48, 2003.
- Codrut¸a Chis¸ and F Cret¸. Solving nonlinear programming problems by linear approximations. 2005.
- Edwin KP Chong and Stanislaw H Zak. An introduction to optimization, volume 76. John Wiley & Sons, 2013.
- Gerard Cornuejols and Reha T¨ut¨unc¨u. Optimization methods in finance, volume 5. Cambridge University Press, 2006.
- Philip E Gill and Elizabeth Wong. Sequential quadratic programming methods. In Mixed integer nonlinear programming, pages 147–224. Springer, 2012.
- Chuan-Hao Guo, Yan-Qin Bai, and Jin-Bao Jian. An improved sequential quadratic programming algorithm for solving general nonlinear programming problems. Journal of Mathematical Analysis and Applications, 409(2):777–789, 2014.
- Magnus R Hestenes. Multiplier and gradient methods. Journal of optimization theory and applications, 4(5):303–320, 1969.
- Magnus Rudolph Hestenes and Eduard Stiefel. Methods of conjugate gradients for solving linear systems, volume 49. NBS Washington, DC, 1952.
- Ming-Hua Lin, John Gunnar Carlsson, Dongdong Ge, Jianming Shi, and Jung-Fa Tsai. A review of piecewise linearization methods. Mathematical problems in Engineering, 2013, 2013.
- R Tyrrell Rockafellar. Augmented lagrange multiplier functions and duality in nonconvex programming. SIAM Journal on Control, 12(2):268–285, 1974.
- Nobuo Sannomiya, Yoshikazu Nishikawa, and Yoshikazu Tsuchihashi. A method for solving nonlinear programming problems by linearization. The transactions of the Institute of Electrical Engineers of Japan. C, 97(1-2):12–18, 1977.
- Claus Still and Tapio Westerlund. A linear programmingbased optimization algorithm for solving nonlinear programming problems. European Journal of Operational Research, 200(3):658–670, 2010.
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