DEGENERATE CASE IN INVESTIGATING CRITICAL POINTS IN TWOVARIABLE ECONOMIC OPTIMIZATION PROBLEMS
Ключевые слова:
Polynomial, partial derivative, determinant, critical point, two-variable function, Taylor series.Аннотация
In economics, most of the optimization problems reduce to finding critical points of an objective function. We present accessible methods such as Taylor expansion and Splitting methods. The proposed approaches are accessible to undergraduate students and researchers encountering degenerate critical points in optimization and mathematical modelling.
Скачивания
Библиографические ссылки
[1] Milnor, J. Morse Theory. Princeton University Press (1963).
[2] Stewart, J. Calculus: Early Transcendentals, 9th ed. Cengage Learning (2020).
[3] Rockafellar, R. T., and Wets, R. J.-B. Variational Analysis. Springer-Verlag (1998).
[4] Mordukhovich, B. S. Variational Analysis and Generalized Differentiation I: Basic Theory. Springer-Verlag (2006).
[5] Mordukhovich, B. S. Variational Analysis and Generalized Differentiation II: Applications. Springer-Verlag (2006).
[6] Andreani, R., Haeser, G., Viana, D. S. "Optimality conditions and global convergence for nonlinear programming." Mathematical Programming, 130(2), 227–254 (2011).
[7] Gfrerer, H., and Mordukhovich, B. S. "Second-order variational analysis of parametric systems and applications." SIAM Journal on Optimization, 23(4), 2405–2432 (2013).
[8] Hirsch, M. W. Differential Topology. Springer-Verlag (1976).
[9] Golubitsky, M., and Guillemin, V. Stable Mappings and Their Singularities. Springer-Verlag (1973).
[10] Lu, G. "The Splitting Lemmas for Nonsmooth Functionals on Hilbert Spaces I." Discrete and Continuous Dynamical Systems, 33, 2939–2990 (2013).
[11] Morse, M. The Calculus of Variations in the Large. American Mathematical Society, (1934).
[12] Greuel, G.-M., and Pfister, G. "The Splitting Lemma in any Characteristic."Journal of Algebra, 689, 610–628 (2026).
[13] Arnold, V. I., Gusein-Zade, S. M., and Varchenko, A. N. Singularities of Differentiable Maps, Vol. 1. Birkhäuser (1985).
[14] Li, H., and Wang, X. "On types of degenerate critical points of real polynomial functions." Journal of Symbolic Computation, 99, 108–126 (2020).
Загрузки
Опубликован
Выпуск
Раздел
Лицензия

Это произведение доступно по лицензии Creative Commons «Attribution» («Атрибуция») 4.0 Всемирная.
License Terms of our Journal


