In this article we study a recently introduced notion of non-smooth analysis, namely convexifactors. We study some properties of the convexifactors and introduce two new chain rules. A new notion of non-smooth pseudoc...
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In this article we study a recently introduced notion of non-smooth analysis, namely convexifactors. We study some properties of the convexifactors and introduce two new chain rules. A new notion of non-smooth pseudoconvex function is introduced and its properties are studied in terms of convexifactors. We also present some optimality conditions for vector minimization in terms of convexifactors.
In this paper, we study the effects of a linear transformation on the partial order relations that are generated by a closed and convex cone in a finite-dimensional space. Sufficient conditions are provided for a tran...
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In this paper, we study the effects of a linear transformation on the partial order relations that are generated by a closed and convex cone in a finite-dimensional space. Sufficient conditions are provided for a transformation preserving a given order. They are applied to derive the relationship between the efficient set of a set and its image under a linear transformation, to characterize generalizedconvex vector functions by using order-preserving transformations, to establish some calculus rules for the subdifferential of a convex vector function, and develop an optimality condition for a convex vector problem.
Let f greater than or equal to 0 be a continuous, concave function on [a, b]. Let (f) over bar = (1/(b - a)) integral(a)(b) f (t) dt. Favard's inequality is that, when delta = (f) over bar 1/2delta integral((f) ov...
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Let f greater than or equal to 0 be a continuous, concave function on [a, b]. Let (f) over bar = (1/(b - a)) integral(a)(b) f (t) dt. Favard's inequality is that, when delta = (f) over bar 1/2delta integral((f) over bar-delta)((f) over bar+delta) psi(u) du greater than or equal to 1/b-a integral(a)(b) psi(f(t)) dt (1) for all convexfunctions, psi, defined on ((f) over bar - delta, (f) over bar + delta). We show there is a delta for which inequality (1) is valid for a class of nonconvexfunctions psi. Further, there is an optimal delta for which the reverse inequality of line (1) is true. The reverse inequality is strictly sharper (in this setting) then Jensen's inequality. (C) 2003 Elsevier Science Ltd. All rights reserved.
generalizedconvex vector functions are characterized by using order preserving transformations and some calculus rules for subdifferential of convex vector functions are obtained.
generalizedconvex vector functions are characterized by using order preserving transformations and some calculus rules for subdifferential of convex vector functions are obtained.
In this paper, we review and unify some classes of generalized convex functions introduced by different authors to prove minimax results in infinite-dimensional spaces and show the relations between these classes. We ...
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In this paper, we review and unify some classes of generalized convex functions introduced by different authors to prove minimax results in infinite-dimensional spaces and show the relations between these classes. We list also for the most general class already introduced by Jeyakumar (Ref. 1) an elementary proof of a minimax result. The proof of this result uses only a finite-dimensional separation theorem;although this minimax result was already presented by Neumann (Ref. 2) and independently by Jeyakumar (Ref. 1), we believe that the present proof is shorter and more transparent.
In this paper, we present sufficient optimality conditions and duality results for a class of nonlinear fractional programming problems. Our results are based on the properties of sublinear functionals and generalized...
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In this paper, we present sufficient optimality conditions and duality results for a class of nonlinear fractional programming problems. Our results are based on the properties of sublinear functionals and generalized convex functions.
It is proved that for a rationally s-convex function continuity and local s-HOLDER-continuity are equivalent at each interior point of the domain of definition of the function. Furthermore, it is shown that a rational...
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A nonlinear multiple objective programming problem is considered where the functions involved are nondifferentiable. By considering the concept of weak minima, the Fritz John type and Karush-Kuhn-Tucker type necessary...
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A nonlinear multiple objective programming problem is considered where the functions involved are nondifferentiable. By considering the concept of weak minima, the Fritz John type and Karush-Kuhn-Tucker type necessary optimality conditions and Wolfe and Mond-Weir type duality results are given in terms of the right differentials of the functions. The duality results are stated by using the concepts of generalized semilocally convexfunctions.
In this paper, (alpha, phi, Q)-invexity is introduced, where alpha: X x X --> int R+m, phi: X x X --> X, X is a Banach space, Q is a convex cone of R(m). This unifies the properties of many classes of functions,...
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In this paper, (alpha, phi, Q)-invexity is introduced, where alpha: X x X --> int R+m, phi: X x X --> X, X is a Banach space, Q is a convex cone of R(m). This unifies the properties of many classes of functions, such as Q-convexity, pseudo-linearity, representation condition, null space condition, and V-invexity. A generalized vector variational inequality is considered, and its equivalence with a multi-objective programming problem is discussed using (alpha, phi, Q)-invexity. An existence theorem for the solution of a generalized vector variational inequality is proved. Some applications of (alpha, phi, Q)-invexity to multi-objective programming problems and to a special kind of generalized vector variational inequality are given.
This paper is a sequel to Ref. 1 in which several kinds of generalized monotonicity were introduced for maps. They were related to generalizedconvexity properties of functions in the case of gradient maps. In the pre...
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This paper is a sequel to Ref. 1 in which several kinds of generalized monotonicity were introduced for maps. They were related to generalizedconvexity properties of functions in the case of gradient maps. In the present paper, we derive first-order characterizations of generalized monotone maps based on a geometrical analysis of generalized monotonicity. These conditions are both necessary and sufficient for generalized monotonicity. Specialized results are obtained for the affine case.
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