REKONSTRUKSI MODEL PROGRAM NONLINIER DENGAN FUNGSI POLINOMIAL MENJADI BENTUK PROGRAM KUADRATIK
DOI:
https://doi.org/10.55606/jurripen.v2i1.814Keywords:
Optimization, Polynomials, Auxiliary Functions, Quadratic ProgrammingAbstract
The purpose of this research to revisits methods that are more effective in nonlinear Optimization with single variable polynomial functions at high degrees. Models with linear objective functions and constraint functions are Polynomials of third, fourth and fifth degree reconstructed into subproblems that are easier to solve, namely quadratic programs, using bilinear Auxiliary Functions and solved by MATLAB simulations. The method used is the development of Tawarmalani & Sahinidis' research regarding relaxation with Auxiliary Functions. Examples of nonlinear Optimization with polynomial functions are also given to illustrate the implementation of this algorithm. The results of the research show that the application of the development reconstruction method produces a global solution that is no better than the solution to the original problem so that it is not an effective alternative method to use.
References
Al-Khayyal, F. A., Larsen, C. & Voorhis, T. V. (1995). A Relaxation Method For Nonconvex Quadratically Constrained Quadratic Programs. Journal of Global Optimization, 6(1): 215-230.
Dixon, L. C. W. (1990). On Finding the Global Minimum of a Function of One Variable. Presented at the SIAM National Meeting, Chicago.
Ferrier, Ch. (1998). Hilbert`s 17th Problem And Best Dual Bounds In Quadratic Minimization. Cybernetics and Systems Analysis, 34(5) : 696-709.
Guenin, B., Konemann, J. & Tuncel, L. (2014). A Gentle Introduction To Optimization. Cambridge : Cambridge University Press.
Hillier, F. S. & Lieberman, G. J. (2001). Introduction to Operations Research, Seventh Edition. New York : The McGraw-Hill Companies, Inc.
Karia, T., Adjiman, C. S. & Chachuat, B. (2022). Assesment Of A Two Step Approach For Global Optimization Of Mixed-Integer Polynomial Programs Using Quadratic Reformulation. Computers and Chemical Engineering, 165(1) : 1- 10.
McCormick, G. P. (1976). Computability Of Global Solutions To Factorable Nonconvex Programs: Part I - Convex Underestimating Problems. Mathematical Programming, 10 (1) : 147 – 175.
Sherali, H. D. & Tuncbilek, C. H. (1992). A Global Optimization Algorithm for Polynomial Programming Problems Using a Reformulation-Linearization Technique. Journal of Global Optimization, 2(1) : 101-112.
Tawarmalani, M. & Sahinidis, N. V. (2004). Global Optimization Of Mixed-Integer Nonlinear Programs: A Theoretical And Computational Study. Mathematical Programming, 99(3) : 563-591.
Tuy, H. (2016). Convex Analysis and Global Optimization, Second Edition. Switzerland : Springer Cham.
Visweswaran, V. & Floudas, C. A. (1990). A Global Optimization Algorithm (GOP) for Certain Classes of Nonconvex NLPs - II. Application of Theory and Test Problems. Computers and Chemical Engineering, 14(12) : 1419-1434.
