SOLVING THE TRANSPORT PROBLEM ON A NETWORK AS NON-LINEAR PROGRAMMING PROBLEM

Tatiana PAŞA

Abstract


In this paper we review the methods that can be applied to solve the non-linear transport problem on a network, formulated as non-linear programming problem. The basic concepts and properties that must be satisfied the functions in order to apply mathematical programming methods are formulated. Algorithms that let us solve problems with differentiable, non-differentiable and separable functions are described.


Keywords


gradient, antigradient, hessian, differentiable functions, non-differentiable functions, separable functions.

Full Text:

PDF

References


DANTZIG, G.B. Aplication of the Simplex Method to a Transportation Problem. În T. C. Koopmans. In: Activity of Production and Allocation. New York: John Wiley and Sons, 1951, p.359 - 373.

ДАНТЦИГ, Д. Линейное программирование, его обобщения и применения. (Г.Н. Андрианова, Л.И. Горькова, & А.А. Корбута, trad.). Москва: ПРОГРЕСС, 1966.

ГОЛЬШТЕЙН, Е., & ЮДИН, В.Д. Задачи линейного программирования транспортного типа. Москва: Наука, 1969.

SARODE, M.V. Application of a Simplex Method to Find the Optimal Solution. In: International Journal of Innovations of Engineering and Science, 2017, vol.2, no.2, p.21-24.

BOHEME, T.J., & FRANK, B. Hybrid Systems, Optimal Control and Hybrid Vehicles. Springer International Publishing AG, 2017.

CAUCHY, A. Méthode générale pour la résolution des systèmes d'équations simultanées. https://gallica.bnf.fr/ ark:/12148/bpt6k2982c/f540.image.langEN. Paris: BACHELIER, IMPRIMEUR - LIBRAIRE, 1847.

KUHN, H.W., & TUCKER, A.W. Nonlinear Programming. Second Berkeley Symposium on Mathematical Statistics and Probability Berkeley: University of California Press, https://projecteuclid.org/euclid.bsmsp/1200500213#toc, 1951, p.481-492.

ROSEN, J.B. The Gradient Projection Method for Nonlinear Programming. Part I. Linear Constraints. In: Journal of the Society for Industrial and Applied Mathematics, 1960, vol.8, no.1, p.181 - 217.

SUN, W., & YUAN, Y.-X. Optimization theory and methods, Nonlinear Programming (vol.1). Springer Science + Business Media, LLC, 2006.

LUENBERGER, D.G., & YE, Y. Linear and nonlinear programming International Series in Operations Research and management science. Stanford: Springer, 2008.

ШОР, Н.З. Методы недифференцируемой оптимизации и сложные экстремальные задачи. Кишинев: Эврика, 2008.

GAMEȚCHI, A., & SOLOMON, D. Cercetări operaționale (vol.II). Chișinău: Evrica, 2015.

MILLER, C.E. The simplex Method for Local Separable Programming. (R.L. Wolfe, Ed.) In: Recent Advances in Mathematical Programming, 1963.

LI, H.-L., & YU, C.-S. A global optimization method for nonconvex separable programming problems. In: European Journal of Operational Research, 1999, vol.117, p.275-292.


Refbacks

  • There are currently no refbacks.