Generalized Preinvex Functions and Their Applications

A class of function called sub-b-s-preinvex function is defined as a generalization of s-convex and b-preinvex functions, and some of its basic properties are presented here. The sufficient conditions of optimality for unconstrainded and inquality constrained programming are discussed under the sub-b-s-preinvexity. Moreover, some new inequalities of the Hermite—Hadamard type for differentiable sub-b-s-preinvex functions are presented. Examples of applications of these inequalities are shown.

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On the Characteristic Properties of Geodesic Sub-$ (\alpha,b,s )$-Preinvex

10.20944/preprints201910.0301.v1 ◽

2019 ◽

Author(s):

Wedad Saleh ◽

Adem Kilicman

Keyword(s):

Sufficient Conditions ◽

Hadamard Manifolds ◽

Basic Properties ◽

Preinvex Functions ◽

New Inequalities

In the present work we study the properties of geodesic sub-$ (\alpha,b,s) $-preinvex functions on Hadamard manifolds and establish some basic properties in both general and differential cases. Further, we study sufficient conditions of optimality and proved some new inequalities under geodesic sub-($ \alpha,b,s $)-preinvexity.

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On some characterizations of sub-b-s-convex functions

Filomat ◽

10.2298/fil1614885l ◽

2016 ◽

Vol 30 (14) ◽

pp. 3885-3895 ◽

Cited By ~ 2

Author(s):

Jiagen Liao ◽

Tingsong Du

Keyword(s):

Convex Functions ◽

Convex Sets ◽

Sufficient Conditions ◽

Generalized Convex Functions ◽

Basic Properties ◽

New Class ◽

Constrained Programming

A new class of generalized convex functions called sub-b-s-convex functions is defined by modulating the definitions of s-convex functions and sub-b-convex functions. Similarly, a new class sub-bs-convex sets, which are generalizations of s-convex sets and sub-b-convex sets, is introduced. Furthermore, some basic properties of sub-b-s-convex functions in both general case and differentiable case are presented. In addition the sufficient conditions of optimality for both unconstrained and inequality constrained programming are established and proved under the sub-b-s-convexity.

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Sufficient Conditions of Isolated Minimizers for Constrained Programming Problems

Numerical Functional Analysis and Optimization ◽

10.1080/01630563.2010.490970 ◽

2010 ◽

Vol 31 (6) ◽

pp. 715-727 ◽

Cited By ~ 5

Author(s):

S. J. Li ◽

S. Xu

Keyword(s):

Sufficient Conditions ◽

Constrained Programming ◽

Isolated Minimizers

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k-Kernel Symmetric Matrices

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/2009/926217 ◽

2009 ◽

Vol 2009 ◽

pp. 1-8 ◽

Cited By ~ 1

Author(s):

A. R. Meenakshi ◽

D. Jaya Shree

Keyword(s):

Scalar Product ◽

Sufficient Conditions ◽

Necessary And Sufficient Conditions ◽

Symmetric Matrices ◽

Fuzzy Matrix ◽

Basic Properties ◽

Necessary And Sufficient

In this paper we present equivalent characterizations ofk-Kernel symmetric Matrices. Necessary and sufficient conditions are determined for a matrix to bek-Kernel Symmetric. We give some basic results of kernel symmetric matrices. It is shown that k-symmetric impliesk-Kernel symmetric but the converse need not be true. We derive some basic properties ofk-Kernel symmetric fuzzy matrices. We obtain k-similar and scalar product of a fuzzy matrix.

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Semi-E-Preinvex Functions

Computer Engineering ◽

10.4018/978-1-61350-456-7.ch311 ◽

2012 ◽

pp. 677-683

Author(s):

Yu-Ru Syau ◽

E. Stanley Lee

Keyword(s):

Nonlinear Programming ◽

Euclidean Space ◽

Convex Functions ◽

Sufficient Conditions ◽

Dimensional Euclidean Space ◽

Quasiconvex Functions ◽

Invex Set ◽

Preinvex Functions ◽

The Relationship ◽

Class Of Functions

A class of functions called semi-E-preinvex functions is defined as a generalization of semi-E-convex functions. Similarly, the concept of semi-E-quasiconvex functions is also generalized to semi-E-prequasiinvex functions. Properties of these proposed classes are studied, and sufficient conditions for a nonempty subset of the n-dimensional Euclidean space to be an E-convex or E-invex set are given. The relationship between semi-E-preinvex and E-preinvex functions are discussed along with results for the corresponding nonlinear programming problems.

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GeodesicB-Preinvex Functions and Multiobjective Optimization Problems on Riemannian Manifolds

Journal of Applied Mathematics ◽

10.1155/2014/524698 ◽

2014 ◽

Vol 2014 ◽

pp. 1-12 ◽

Cited By ~ 3

Author(s):

Sheng-lan Chen ◽

Nan-Jing Huang ◽

Donal O'Regan

Keyword(s):

Multiobjective Optimization ◽

Riemannian Manifolds ◽

Optimization Problems ◽

Sufficient Conditions ◽

Properly Efficient Solution ◽

Invex Functions ◽

Multiobjective Optimization Problems ◽

Dual Programming ◽

Preinvex Functions ◽

Primal And Dual

We introduce a class of functions called geodesicB-preinvex and geodesicB-invex functions on Riemannian manifolds and generalize the notions to the so-called geodesic quasi/pseudoB-preinvex and geodesic quasi/pseudoB-invex functions. We discuss the links among these functions under appropriate conditions and obtain results concerning extremum points of a nonsmooth geodesicB-preinvex function by using the proximal subdifferential. Moreover, we study a differentiable multiobjective optimization problem involving new classes of generalized geodesicB-invex functions and derive Kuhn-Tucker-type sufficient conditions for a feasible point to be an efficient or properly efficient solution. Finally, a Mond-Weir type duality is formulated and some duality results are given for the pair of primal and dual programming.

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ON A NEW CLASS OF IMPLICATIONS: (g,min)-IMPLICATIONS AND SEVERAL CLASSICAL TAUTOLOGIES

International Journal of Uncertainty Fuzziness and Knowledge-Based Systems ◽

10.1142/s0218488512500018 ◽

2012 ◽

Vol 20 (01) ◽

pp. 1-20 ◽

Cited By ~ 14

Author(s):

HUA-WEN LIU

Keyword(s):

Classical Logic ◽

Functional Equations ◽

Sufficient Conditions ◽

Necessary And Sufficient Conditions ◽

Triangular Norms ◽

Basic Properties ◽

New Class ◽

Fuzzy Implications ◽

Necessary And Sufficient

A new class of fuzzy implications, called (g, min )-implications, is introduced by means of the additive generators of continuous Archimedean t-conorms, called g-generators. Basic properties of these implications are discussed. It is shown that the (g, min )-implications are really a new class different from the known ( S , N )-, R -, QL - and Yager's f- and g-implications. Generalizations of three classical logic tautologies with implications, viz. law of importation, contraction law and distributivity over triangular norms ( t -norms) and triangular conorms ( t -conorms) are investigated. A series of necessary and sufficient conditions are proposed, under which the corresponding functional equations are satisfied.

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Semi-E-Preinvex Functions

International Journal of Artificial Life Research ◽

10.4018/jalr.2010070103 ◽

2010 ◽

Vol 1 (3) ◽

pp. 31-39

Author(s):

Yu-Ru Syau ◽

E. Stanley Lee

Keyword(s):

Nonlinear Programming ◽

Euclidean Space ◽

Nonempty Subset ◽

Sufficient Conditions ◽

Dimensional Euclidean Space ◽

Quasiconvex Functions ◽

Invex Set ◽

Preinvex Functions ◽

The Relationship ◽

Class Of Functions

A class of functions called semi--preinvex functions is defined as a generalization of semi--convex functions. Similarly, the concept of semi--quasiconvex functions is also generalized to semi--prequasiinvex functions. Properties of these proposed classes are studied, and sufficient conditions for a nonempty subset of the -dimensional Euclidean space to be an -convex or -invex set are given. The relationship between semi--preinvex and -preinvex functions are discussed along with results for the corresponding nonlinear programming problems.

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EXTENSIONS OF THE HERMITE–HADAMARD INEQUALITY FOR -PREINVEX FUNCTIONS ON AN INVEX SET

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972716001374 ◽

2017 ◽

Vol 95 (3) ◽

pp. 412-423 ◽

Cited By ~ 1

Author(s):

DAH-YAN HWANG ◽

SILVESTRU SEVER DRAGOMIR

Keyword(s):

Sufficient Conditions ◽

Necessary And Sufficient Conditions ◽

Hadamard Inequality ◽

Invex Set ◽

Preinvex Functions ◽

Necessary And Sufficient

Necessary and sufficient conditions to characterise weakly $r$-preinvex functions on an invex set are obtained and used to establish generalisations of the Hermite–Hadamard inequality for such functions.

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Non-strict don't care algebras and specifications

Mathematical Structures in Computer Science ◽

10.1017/s0960129500000888 ◽

1996 ◽

Vol 6 (1) ◽

pp. 85-125 ◽

Cited By ~ 1

Author(s):

Egidio Astesiano ◽

Maura Cerioli

Keyword(s):

Computer Science ◽

Essential Role ◽

Sufficient Conditions ◽

Appropriate Use ◽

Partial Case ◽

Basic Properties ◽

Algebraic Specifications ◽

Algebraic Framework ◽

Necessary And Sufficient ◽

The Relationship

Non-strict don't care functions, whose foremost representative is the ubiquitous if_then_else, play an essential role in computer science. As far as the semantics is concerned, they can be modelled by their totalizations with the appropriate use of elements representing undefinedness, as D. Scott has shown in his denotational approach. The situation is not so straightforward when we consider non-strict functions in the context of an algebraic framework; this point is discussed in the last section, where we explore the relationship between non-strict don't care and total algebras. The central part of this paper, after presenting the basic properties of the category of non-strict algebras, is an investigation of conditional algebraic specifications. It is shown that non-strict conditional specifications are equivalent to disjunctive specifications, and necessary and sufficient conditions for the existence of initial models are given. Since non-strict don't care specifications generalize both the total and the partial case, it is shown how the results for initiality can be obtained as specializations.

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