Results 21 to 30 of about 59 (56)
Journal of Applied Mathematics, Volume 2011, Issue 1, 2011., 2011 A nondifferentiable multiobjective optimization problem with nonempty set constraints is considered, and the equivalence of weakly efficient solutions, the critical points for the nondifferentiable multiobjective optimization problems, and solutions for vector variational‐like inequalities is established under some suitable conditions. Nonemptiness and
Xin-kun Wu +3 more
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On Properties of Geodesic η‐Preinvex Functions
Advances in Operations Research, Volume 2009, Issue 1, 2009., 2009 The present paper deals with the properties of geodesic η‐preinvex functions and their relationships with η‐invex functions and strictly geodesic η‐preinvex functions. The geodesic η‐pre‐pseudo‐invex and geodesic η‐pre‐quasi‐invex functions on the geodesic invex set are introduced and some of their properties are discussed.
I. Ahmad +3 more
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Continuous‐Time Multiobjective Optimization Problems via Invexity
Abstract and Applied Analysis, Volume 2007, Issue 1, 2007., 2007 We introduce some concepts of generalized invexity for the continuous‐time multiobjective programming problems, namely, the concepts of Karush‐Kuhn‐Tucker invexity and Karush‐Kuhn‐Tucker pseudoinvexity. Using the concept of Karush‐Kuhn‐Tucker invexity, we study the relationship of the multiobjective problems with some related scalar problems.
Valeriano A. De Oliveira +2 more
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Generalized preinvex functions and their properties
International Journal of Stochastic Analysis, Volume 2006, Issue 1, 2006., 2006 We introduce some new classes of preinvex and invex functions, which are called ϕ‐preinvex and ϕ‐invex functions. We study some properties of these classes of ϕ‐preinvex (ϕ‐invex) functions. In particular, we establish the equivalence among the ϕ‐preinvex functions, ϕ‐invex functions, and ϕη‐monotonicity of their differential under some suitable ...
Muhammad Aslam Noor, Khalida Inayat Noor
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International Journal of Stochastic Analysis, Volume 2006, Issue 1, 2006., 2006 A class of multiobjective variational control and multiobjective fractional variational control problems is considered, and the duality results are formulated. Under pseudoinvexity assumptions on the functions involved, weak, strong, and converse duality theorems are proved.
C. Nahak
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International Journal of Mathematics and Mathematical Sciences, Volume 2005, Issue 8, Page 1253-1276, 2005., 2005 We first define a new class of generalized convex n‐set functions, called (𝔉, b, ϕ, ρ, θ)‐univex functions, and then establish a fairly large number of global parametric sufficient optimality conditions under a variety of generalized (𝔉, b, ϕ, ρ, θ)‐univexity assumptions for a discrete minmax fractional subset programming problem.
G. J. Zalmai
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International Journal of Mathematics and Mathematical Sciences, Volume 2005, Issue 6, Page 949-973, 2005., 2005 A fairly large number of global semiparametric sufficient efficiency results are established under various generalized (ℱ, b, φ, ρ, θ)‐univexity assumptions for a multiobjective fractional subset programming problem.
G. J. Zalmai
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Multiobjective duality with ρ − (η, θ)‐invexity
International Journal of Stochastic Analysis, Volume 2005, Issue 2, Page 175-180, 2005., 2005 Under ρ − (η, θ)‐invexity assumptions on the functions involved, weak, strong, and converse duality theorems are proved to relate properly efficient solutions of the primal and dual problems for a multiobjective programming problem.
C. Nahak, S. Nanda
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Role of exponential type random invexities for asymptotically sufficient efficiency conditions in semi-infinite multi-objective fractional programming. [PDF]
Springerplus, 2016 Verma RU, Seol Y.
europepmc +1 more source
A class of generalized invex functions and vector variational-like inequalities. [PDF]
J Inequal Appl, 2017 Li R, Yu G.
europepmc +1 more source