Results 61 to 70 of about 6,202,679 (144)

On locally Lipschitz vector-valued invex functions [PDF]

Bulletin of the Australian Mathematical Society, 1993
The four types of invexity for locally Lipschitz vector-valued functions recently introduced by T. W. Reiland are studied in more detail. It is shown that the class of restricted K-invex in the limit functions is too large to obtain desired optimisation theorems and the other three classes are contained in the class of functions which are invex 0 in ...
Yen, N. D., Sach, P. H.
openaire   +2 more sources

An Estimation of Different Kinds of Integral Inequalities for a Generalized Class of Godunova–Levin Convex and Preinvex Functions via Pseudo and Standard Order Relations

Journal of Function Spaces, Volume 2025, Issue 1, 2025.
The connection between generalized convexity and analytic operators is deeply rooted in functional analysis and operator theory. To put the ideas of preinvexity and convexity even closer together, we might state that preinvex functions are extensions of convex functions. Integral inequalities are developed using different types of order relations, each
Zareen A. Khan, Waqar Afzal, Nikhil Khanna   +2 more
wiley   +1 more source

Some Novel Inequalities for Godunova–Levin Preinvex Functions via Interval Set Inclusion (⊆) Relation

Journal of Mathematics, Volume 2025, Issue 1, 2025.
In this note, we introduce the concept of ℏ‐Godunova–Levin interval‐valued preinvex functions. As a result of these novel notions, we have developed several variants of Hermite–Hadamard and Fejér‐type inequalities under inclusion order relations. Furthermore, we demonstrate through suitable substitutions that this type of convexity unifies a variety of
Zareen A. Khan, Waqar Afzal, Mujahid Abbas, Kwara Nantomah, Ding-Xuan Zhou   +4 more
wiley   +1 more source

PROPER AND ISOLATED EFFICIENCIES IN MULTIOBJECTIVE OPTIMIZATION PROBLEMS

Tạp chí Khoa học Đại học Đà Lạt, 2012
We employ some advanced tools of variational analysis and generalised differentiation such as the nonsmooth version of Fermat's rule, the limiting sub-differential of maximum functions, and the sum rules for the Frechet and Mordukhovich sub-differentials
Thái Doãn Chương
doaj   +1 more source

Some Hermite–Hadamard Type Inequality for the Operator p,P‐Preinvex Function

Journal of Mathematics, Volume 2025, Issue 1, 2025.
The goal of the article is to introduce the operator p,P‐preinvex function and present several features of this function. Also, we establish some Hermite–Hadamard type inequalities for this function.
Mahsa Latifi Moghadam, Omid Pourbahri Rahpeyma, Davood Ebrahimi Bagha, Pramita Mishra   +3 more
wiley   +1 more source

Criterion for Generalized Weakly Fuzzy Invex Monotonocities

, 2018
The present paper deals with the concepts of generalized fuzzy invex monotonocities and generalized weakly fuzzy invex functions. Some necessary conditions for weakly fuzzy invex monotonocities are presented.
Meraj A. Khan, Izhar Ahmad, Abdulrahman Aljohani   +2 more
core   +1 more source

Robustness and exploration of variational and machine learning approaches to inverse problems: An overview

GAMM-Mitteilungen, Volume 47, Issue 4, November 2024.
Abstract This paper provides an overview of current approaches for solving inverse problems in imaging using variational methods and machine learning. A special focus lies on point estimators and their robustness against adversarial perturbations. In this context results of numerical experiments for a one‐dimensional toy problem are provided, showing ...
Alexander Auras, Kanchana Vaishnavi Gandikota, Hannah Droege, Michael Moeller   +3 more
wiley   +1 more source

INFINITELY MANY INVEX FUNCTIONS WITHOUT CONVEXITY

Bulletin of informatics and cybernetics
The paper under review provides several examples of smooth and nonsmooth invex functions that are not necessarily convex. However, as the authors themselves mention, invexity has not yet found a significant application in mathematical optimization (or in any other field).
Shiraishi, Shunsuke, Obata, Tsuneshi, Yokoyama, Kazunori   +2 more
openaire   +3 more sources

In Vitro Effect of Anodization of Titanium Abutments on Color Parameters and Color Difference of Lithium Disilicate All‐Ceramic Crowns

Clinical and Experimental Dental Research, Volume 10, Issue 5, October 2024.
ABSTRACT Objective This study assessed the effect of the anodization of titanium abutments on the color parameters and color difference of lithium disilicate (LDS) all‐ceramic crowns. Materials and Methods In this study, 19 straight abutments were divided into two groups: anodized (n = 9) and non‐anodized control (n = 9), with one hybrid zirconia ...
Sotude Khorshidi, Arash Zarbakhsh, Shirin Lawaf, Shaghayegh Golalipour, Maryam Sayyari, Alireza Mahmoudi Nahavandi   +5 more
wiley   +1 more source

Optimality Condition and Wolfe Duality for Invex Interval-Valued Nonlinear Programming Problems [PDF]

, 2013
The concepts of preinvex and invex are extended to the interval-valued functions. Under the assumption of invexity, the Karush-Kuhn-Tucker optimality sufficient and necessary conditions for interval-valued nonlinear programming problems are derived ...
Jianke Zhang
core   +1 more source