44 research outputs found
SOME PROPERTIES OF EXPONENTIALLY PREINVEX FUNCTIONS
In this paper, we introduce some new concepts of the exponentially preinvex functions. We investigate several properties of the exponentially preinvex functions and discuss their relations with convex functions. Optimality conditions are characterized by a class of variational-like inequalities. Several interesting results characterizing the exponentially preinvex functions are obtained. Results obtained in this paper can be viewed as significant improvement of previously known results
A critical view on invexity
The aim of this note is to emphasize the fact that in many papers on invexity
published in prestigious journals there are not clear definitions, trivial or
not clear statements and wrong proofs. We also point out the unprofessional way
of answering readers' questions by some authors. We think that this is caused
mainly by the lack of criticism of the invexity communityComment: The paper was submitted to JOTA in December 2007 and practically
accepted by the AE handling it in March 2008. Being a critical paper, the EiC
asked the authors of the criticised articles to say their opinion. With the
change of the EiC's, apparently the paper was not transmitted to the new Ei
Semistrict -Preinvexity and Optimality in Nonlinear Programming
A class of semistrictly -preinvex functions and optimality in
nonlinear programming are further discussed. Firstly, the relationships between semistrictly
-preinvex functions and -preinvex functions are further discussed. Then, two interesting
properties of semistrictly -preinvexity are given. Finally, two optimality results for nonlinear programming problems are obtained under the assumption of semistrict -preinvexity. The obtained results are new and different from the corresponding ones in the literature. Some examples are given to illustrate our results
Integral Transformation, Operational Calculus and Their Applications
The importance and usefulness of subjects and topics involving integral transformations and operational calculus are becoming widely recognized, not only in the mathematical sciences but also in the physical, biological, engineering and statistical sciences. This book contains invited reviews and expository and original research articles dealing with and presenting state-of-the-art accounts of the recent advances in these important and potentially useful subjects
Preinvex functions and weak efficient solutions for some vectorial optimization problem in Banach spaces
AbstractIn this work, we introduce the notion of preinvex function for functions between Banach spaces. By using these functions, we obtain necessary and sufficient conditions of optimality for vectorial problems with restrictions of inequalities. Moreover, we will show that this class of problems has the property that each local optimal solution is in fact global
Existence of solutions for vector optimization
AbstractIn this paper, we prove the existence of a weak minimum for constrained vector optimization problem by making use of vector variational-like inequality and preinvex functions
NEW ASPECTS OF STRONGLY Log-PREINVEX FUNCTIONS
In this paper, we consider some new classes of log-preinvex functions. Several properties of the log-preinvex functions are studied. We also discuss their relations with convex functions. Several interesting results characterizing the log-convex functions are obtained. Optimality conditions of differentiable strongly -preinvex are characterized by a class of variational-like inequalities. Results obtained in this paper can be viewed as significant improvement of previously known results
Duality in Fractional Programming Involving Locally Arcwise Connected and Related Functions
A nonlinear fractional programming problem is considered, where the functions involved are diferentiable with respect to an arc.Necessary and su±cient optimality conditions are obtained in terms of the right diferentials with respect to an arc of the functions. A dual is formulated and duality results are proved using concepts of locally arcwise connected, locally Q-connected and locally P-connected functions .Our results generalize the results obtained by Lyall, Suneja and Aggarwal, Kaul and Lyall and Kaul et.al.Generalized convexity; Fractional programming; Optimality conditions, Duality