Results 11 to 20 of about 59 (56)
Sufficiency and Duality for Multiobjective Programming under New Invexity
Mathematical Problems in Engineering, Volume 2016, Issue 1, 2016., 2016 A class of multiobjective programming problems including inequality constraints is considered. To this aim, some new concepts of generalized (F, P)‐type I and (F, P)‐type II functions are introduced in the differentiable assumption by using the sublinear function F.
Yingchun Zheng +2 more
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Integral Majorization Theorem for Invex Functions
Abstract and Applied Analysis, Volume 2014, Issue 1, 2014., 2014 We obtain some general inequalities and establish integral inequalities of the majorization type for invex functions. We give applications to relative invex functions.
M. Adil Khan +3 more
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International Journal of Mathematics and Mathematical Sciences, Volume 2014, Issue 1, 2014., 2014 We study a nonlinear multiple objective fractional programming with inequality constraints where each component of functions occurring in the problem is considered semidifferentiable along its own direction instead of the same direction. New Fritz John type necessary and Karush‐Kuhn‐Tucker type necessary and sufficient efficiency conditions are ...
Hachem Slimani +2 more
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Geodesic B‐Preinvex Functions and Multiobjective Optimization Problems on Riemannian Manifolds
Journal of Applied Mathematics, Volume 2014, Issue 1, 2014., 2014 We introduce a class of functions called geodesic B‐preinvex and geodesic B‐invex functions on Riemannian manifolds and generalize the notions to the so‐called geodesic quasi/pseudo B‐preinvex and geodesic quasi/pseudo B‐invex functions. We discuss the links among these functions under appropriate conditions and obtain results concerning extremum ...
Sheng-lan Chen +3 more
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Abstract and Applied Analysis, Volume 2014, Issue 1, 2014., 2014 We first obtain that subdifferentials of set‐valued mapping from finite‐dimensional spaces to finite‐dimensional possess certain relaxed compactness. Then using this weak compactness, we establish gap functions for generalized Stampacchia vector variational‐like inequalities which are defined by means of subdifferentials.
Yanfei Chai +3 more
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International Journal of Mathematics and Mathematical Sciences, Volume 2013, Issue 1, 2013., 2013 We establish properly efficient necessary and sufficient optimality conditions for multiobjective fractional programming involving nonsmooth generalized (ℱ, b, ϕ, ρ, θ)‐univex functions. Utilizing the necessary optimality conditions, we formulate the parametric dual model and establish some duality results in the framework of generalized (ℱ, b, ϕ, ρ, θ)
Jen-Chwan Liu +2 more
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A Class of Fuzzy Variational Inequality Based on Monotonicity of Fuzzy Mappings
Abstract and Applied Analysis, Volume 2013, Issue 1, 2013., 2013 Invex monotonicity and pseudoinvex monotonicity of fuzzy mappings are introduced in this paper, and relations are discussed between invex monotonicity (pseudoinvex monotonicity) and invexity (pseudoinvexity) of fuzzy mappings. The existence of a solution to the fuzzy variational‐like inequality is discussed, and the existence theorem can be achieved ...
Zezhong Wu, Jiuping Xu, Kanishka Perera
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Generalized Differentiable E‐Invex Functions and Their Applications in Optimization
Advances in Operations Research, Volume 2012, Issue 1, 2012., 2012 The concept of E‐convex function and its generalizations is studied with differentiability assumption. Generalized differentiable E‐convexity and generalized differentiable E‐invexity are used to derive the existence of optimal solution of a general optimization problem.
S. Jaiswal, G. Panda, Chandal Nahak
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On a Nonsmooth Vector Optimization Problem with Generalized Cone Invexity
Abstract and Applied Analysis, Volume 2012, Issue 1, 2012., 2012 By using Clarke’s generalized gradients we consider a nonsmooth vector optimization problem with cone constraints and introduce some generalized cone‐invex functions called K‐α‐generalized invex, K‐α‐nonsmooth invex, and other related functions. Several sufficient optimality conditions and Mond‐Weir type weak and converse duality results are obtained ...
Hehua Jiao, Sanyang Liu, Ferenc Hartung
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Higher‐Order Generalized Invexity in Control Problems
Journal of Control Science and Engineering, Volume 2011, Issue 1, 2011., 2011 We introduce a higher‐order duality (Mangasarian type and Mond‐Weir type) for the control problem. Under the higher‐order generalized invexity assumptions on the functions that compose the primal problems, higher‐order duality results (weak duality, strong duality, and converse duality) are derived for these pair of problems.
S. K. Padhan, C. Nahak, Onur Toker
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