Second-ordered Characterization of Generalized Convex Functions and Their Applications in Optimization Problems

Document Type : Original Research Articles

Authors
Mohammad Taghi Nadi 1
Jafar Zafarani 2
1 School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P. O. Box 19395-5746, Tehran, Islamic Republic of Iran
2 2 Department of Mathematics, Sheikhbahaee University and University of Isfahan, Isfahan, Islamic Republic of Iran
10.22059/jsciences.2025.389419.1007912
Abstract
This survey investigates some developments in the second-order characterization of generalized convex functions using the coderivative of subdifferential mapping. More precisely, it presents the second-order characterization for quasiconvex, pseudoconvex and invex functions. Furthermore, it gives some applications of the second-order subdifferentials in optimization problems such as constrained and unconstrained nonlinear programming.
Keywords
Second-order subdifferential
Positive semidefinite property
Regular second-order subdifferential
Second-order optimality conditions
Subjects
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Journal of Sciences, Islamic Republic of Iran
Volume 35, Issue 3
Summer 2024
Pages 267-277