In this paper, we have developed a method from which we can determine the exact optimal solution to geometric programming problems (GPPs). The method is based on the determination of exact rows of the optimal matrix in a GPP. The optimal matrix is the final matrix used to determine the optimal primal decision variables that satisfy the optimal objective function. This matrix is very important as it eliminates the rule of thumb and enables the accuracy of the solution to GPPs.

geometric programming problems, applied mathematics, optimal matrix, Moore-Penrose g-inverse, urban and regional planning.

Received: February 24, 2024; Accepted: April 12, 2024; Published: July 16, 2024

How to cite this article: Harrison O. Amuji, Fidelis I. Ugwuowo, Christy C. Nwachi, Bridget N. Okechukwu and Immaculata O. Okeoma, On exact optimal solution to geometric programming problems, Advances and Applications in Discrete Mathematics 41(5) (2024), 429-439. https://doi.org/10.17654/0974165824029

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

References:

[1] H. O. Amuji, C. C. Nwachi, B. N. Okechukwu, I. O. Okeoma and S. A. Inah, Approximating linear programming by geometric programming and its application to urban planning, African Journal of Mathematics and Statistics Studies 6 (2023), 115-127.
[2] M. Avriel and A. C. Williams, Complimentary geometric programming, SIAM J. Appl. Math. 19 (1970), 125-141.
[3] S. Boyd, J. K. Seung, V. Lieven and H. A. Arash, A tutorial on geometric programming, Optim. Eng. 8 (2007), 67-127.
[4] R. J. Duffin, Linearizing geometric programs, SIAM Rev. 12 (1970), 211-227.
[5] Y. A. Abbas and H. E. Khalid, On multi-objective geometric programming problems with a negative degree of difficulty, Iraqi Journal of Statistical Science 21 (2012), 1-14.
[6] R. C. Rao, A note on a generalized inverse of a matrix with applications to problems in mathematical statistics, J. Roy. Statist. Soc. Ser. B 24 (1962), 152-158.
[7] H. O. Amuji, G. U. Ugwuanyim and O. C. Nwosu, A solution to geometric programming problems with negative degrees of difficulty, Advances and Applications in Discrete Mathematics 26(2) (2021), 221-230.
[8] H. O. Amuji, F. I. Ugwuowo, W. I. E. Chukwu and P. I. Uche, A modified generalised inverse method for solving geometric programming problems with extended degrees of difficulties Int. J. Oper. Res. 38 (2020), 19-30.
[9] J. G. Ecker, Geometric programming methods, computations and applications, SIAM Rev. 22 (1980), 338-362.