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Global nonparametric sufficient optimality conditions for semi-infinite discrete minmax fractional programming problems involving generalized (η,ρ)-invex functions

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NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION 2007年第1-2期28卷 173-209页

作者： Zalmai, G. J. Zhang, Qinghong No Michigan Univ Dept Math & Comp Sci Marquette MI 49855 USA

In this paper, we establish a set of necessary optimality conditions and discuss a fairly large number of sets of global nonparametric sufficient optimality criteria under various generalized (eta, rho)-invexity assumptions for a minmax fractional programming problem with infinitely many nonlinear inequality and equality constraints.

关键词： discrete minmax fractional programming generalized invex functions infinitely many equality and inequality constraints semi-infinite programming sufficient optimality conditions

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Parametric Duality Models for Semiinfinite Multiobjective Fractional Programming Problems Containing generalized (α, η, ρ)-V-invex functions

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Acta Mathematicae Applicatae Sinica 2013年第2期29卷 225-240页

作者： G.J. ZALMAI Qing-hong ZHANG Department of Mathematics and Computer Science Northern Michigan University

In this paper, we present several parametric duality results under various generalized （a,v,p）-V- invexity assumptions for a semiinfinite multiobjective fractional programming problem.

关键词： Semiinfinite programming multiobjective fractional programming generalized invex functions infinitely many equality and inequality constraints parametric duality models duality theorems

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Nonparametric duality models for semi-infinite discrete minmax fractional programming problems involving generalized (η,ρ)-invex functions

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NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION 2007年第1-2期28卷 211-243页

作者： Zalmai, G. J. Zhang, Qinghong No Michigan Univ Dept Math & Comp Sci Marquette MI 49855 USA

In this paper, we discuss a fairly large number of nonparametric duality results under various generalized (eta, rho)-invexity assumptions for a semi-infinite minmax fractional programming problem.

关键词： discrete minmax fractional programming duality models duality theorems generalized invex functions infinitely many equality and inequality constraints semi-infinite programming

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generalized invexity and generalized invariant monotonicity

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2003年第3期117卷 607-625页

作者： Yang, XM Yang, XQ Teo, KL Chongqing Normal Univ Dept Math Chongqing Peoples R China Hong Kong Polytech Univ Dept Appl Math Kowloon Hong Kong Peoples R China

In this paper, several kinds of invariant monotone maps and generalized invariant monotone maps are introduced. Some examples are given which show that invariant monotonicity and generalized invariant monotonicity are proper generalizations of monotonicity and generalized monotonicity. Relationships between generalized invariant monotonicity and generalized invexity are established. Our results are generalizations of those presented by Karamardian and Schaible.

关键词： invariant monotone maps generalized invariant monotone maps invex functions generalized invex functions

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Invariant monotone vector fields on Riemannian manifolds

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NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS 2009年第5期70卷 1850-1861页

作者： Barani, A. Pouryayevali, M. R. Univ Isfahan Dept Math Esfahan Iran

Various concepts of invariant monotone vector fields on Riemannian manifolds are introduced. Some examples of invariant monotone vector fields are given. Several notions of invexities for functions on Riemannian manifolds are defined and their relations with invariant monotone vector fields are studied. (C) 2008 Elsevier Ltd. All rights reserved.

关键词： generalized invex functions Monotone vector fields Invariant monotone vector fields Riemannian manifolds

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generalized invariant monotonicity and invexity of non-differentiable functions

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JOURNAL OF GLOBAL OPTIMIZATION 2006年第4期36卷 537-564页

作者： Jabarootian, T. Zafarani, J. Univ Isfahan Dept Math Esfahan 81745163 Iran

This paper is devoted to the study of relationships between several kinds of generalized invexity of locally Lipschitz functions and generalized monotonicity of corresponding Clarke's subdifferentials. In particular, some necessary and sufficient conditions of being a locally Lipschitz function invex, quasiinvex or pseudoinvex are given in terms of momotonicity, quasimonotonicity and pseudomonotonicity of its Clarke's subdifferential, respectively. As an application of our results, the existence of the solutions of the variational-like inequality problems as well as the mathematical programming problems (MP) is given. Our results extend and unify the well known earlier works of many authors.

关键词： generalized invariant monotone generalized invex functions Clarke's subdifferential variational-like problem mathematical programming problem

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Criteria for generalized invex monotonicities

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2005年第1期164卷 115-119页

作者： Yang, XM Yang, XQ Teo, KL Hong Kong Polytech Univ Dept Appl Math Kowloon Hong Kong Peoples R China Chongqing Normal Univ Dept Math Chongqing 400047 Peoples R China

In this paper, under appropriate conditions, we establish that (i) if the gradient of a function is (strictly) pseudo-monotone, then the function is (strictly) pseudo-invex;(ii) if the gradient of a function is quasi-monotone, then the function is quasi-invex;and (iii) if the gradient of a function is strong pseudo-monotone, then the function is strong pseudo-invex. (C) 2003 Elsevier B.V. All rights reserved.

关键词： generalized invex monotonicity generalized invex functions mathematical programming

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Criteria for generalized invex monotonicities without Condition C

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2006年第2期170卷 667-671页

作者： Peng, JW Chongqing Normal Univ Fac Math & Comp Sci Chongqing 400047 Peoples R China

In this paper, some necessary conditions of (strictly) pseudo-invex monotonicity and quasi-invex monotonicity are established with the condition that eta is affine in the first argument and skew instead of Condition C... 详细信息

关键词： generalized invex monotonicity generalized invex functions mathematical programming afline

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Nonsmooth multiobjective fractional programming with generalized invexity

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TAIWANESE JOURNAL OF MATHEMATICS 2006年第2期10卷 467-478页

作者： Kim, DS Pukyong Natl Univ Dept Appl Math Pusan 608737 South Korea

In this paper, we consider nonsmooth multiobjective fractional programming problems involving locally Lipschitz functions. We introduce the property of generalized invexity for fractional function. We present necessary optimality conditions, sufficient optimality conditions and duality relations for nonsmooth multiobjective fractional programming problems, which is for a weakly efficient solution under suitable generalized invexity assumptions.

关键词： multiobjective fractional programming generalized invex functions optimality conditions duality theorems

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