Higher-Order Optimality Conditions for Degenerate Unconstrained Optimization Problems

Autor:	Viktor Zadachyn
Jazyk:	angličtina
Rok vydání:	2022
Předmět:	unconditional optimization degenerate minimum point optimality conditions multilinear form Mathematics QA1-939
Zdroj:	Journal of Optimization, Differential Equations and Their Applications, Vol 30, Iss 1, Pp 88-97 (2022)
Druh dokumentu:	article
ISSN:	2617-0108 2663-6824
DOI:	10.15421/142204
Popis:	In this paper necessary and sufficient conditions of a minimum for the unconstrained degenerate optimization problem are presented. These conditions generalize the well-known optimality conditions. The new optimality conditions are presented in terms of polylinear forms and Hesse’s pseudoinverse matrix. The results are illustrated by examples.The formulation and appearance of these conditions differ from high-order optimality conditions by other authors. The suggested representation of high-order optimality conditions makes them convenient for the evaluation of the convergence rate for unconstrained optimization methods in the case of a singular minimum point, for example, for the analysis of Newton’s and quasi-Newton’s methods.
Databáze:	Directory of Open Access Journals
Externí odkaz:	https://doaj.org/article/db9b958f7492463a86b5e1ea1ffcb953 Zobrazit plný text záznamu View record in DOAJ