-Invexity
Mixed Saddle Point and Its Equivalence with an Efficient Solution under Generalized (V, p) Invexity
... invexity for nonsmooth vector-valued Lipschitz functions using Clarke’s generalized subgradients and established duality results for multiobjective programming problems. Bhatia [9] introduced higher order strong ...
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Sufficiency and duality in nondifferentiable multiobjective programming involving higher order strong invexity
... Agarwal et al. [] presented the optimality and duality results for multiobjective op- timization problems involving locally Lipschitz functions and type I invexity. In [], Bae et al. formulated ...
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Nondifferentiable mathematical programming involving (G,β) invexity
... To further enlarge the class of mathematical models for which the theoretical tools hold, Antczak extended the invexity to G-invexity [] for scalar differentiable functions. In the natural way, he extended ...
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Duality in nondifferentiable minimax fractional programming with B (p, r) invexity
... of invexity and estab- lished Karush-Kuhn-Tucker type sufficient optimality conditions for nonlinear programming ...Generalized invexity and duality for multiobjective programming problems are discussed in ...
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Strict global minimizers and higher order generalized strong invexity in multiobjective optimization
... Higher-order strict minimizers with respect to a nonlinear function for a multiobjective optimization problem are introduced and are characterized via sufficient optimality conditions and higher-order mixed saddle points ...
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Generalized invexity and invariant monotonicity
... of invexity was introduced by Hanson [2], where it is shown that the Kuhn-Tucker conditions are sufficient for (global) optimality of non-linear programming problems under invexity ...
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Generalized Invexity of Higher Order and Its Applications in Variational Problems
... (2) If ξ ( t x x , , ) = η ( t x x , , ) = − x x , the definition 2.1 reduces to the definition of ρ-convexity of order m. (3) Definition of invexity of order m given by Bhatia and Sahay [11] is a particular case ...
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Generalized Invariant Monotonicity and Generalized Invexity of Nondifferentiable Functions
... In 9, sufficient conditions for ρ, θ-η invariant quasimonotone for Fr´echet differ- entiable functions were given. However, necessary conditions have been missing. In what follows, we will give the necessary conditions for ...
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New Integral Inequalities through Invexity with Applications
... In this paper, we obtain some inequalities of Simpson’s inequality type for functions whose derivatives absolute values are quasi-preinvex func- tion.. Applications to some special means[r] ...
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Generalization of integral inequalities of the type of Hermite-Hadamard through invexity
... Dragomir, Refinements of Hermite-Hadamard type inequality for functions whose second derivatives absolute values are quasiconvex, RGMIA Research Report Collection , Vol.. Kim, Inequaliti[r] ...
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On the characteristic properties of geodesic sub- α, b, s -preinvex
... geodesic invexity in Riemannian manifold was introduced and preinvexity on a geodesic invex set were defined, further the relation- ship between geodesic invexity and preinvexity on manifolds was studied by ...
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On Second Order Duality in Nondifferentiable Continuous Programming
... A Mond-Weir type second-order dual continuous programming problem associated with a class of nondifferentiable continuous programming problems is formulated. Under second-order pseudo-invexity and second-order ...
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Optimality Conditions and Second Order Duality for Nondifferentiable Multiobjective Continuous Programming Problems
... Second-order duality in mathematical programming has been extensively investigated in the literature. In [1], Chen formulated second order dual for a constrained variational problem and established various duality re- ...
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On Mixed Type Duality for Nondifferentiable Multiobjective Variational Problems
... Before stating our mixed type multiobjective variational problem, we mention the follow- ing conventions for vectors x and y in n-dimensional Euclidian space R n to be used through- out the analysis of this research ...
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New classes of generalized invex monotonicity
... monotonicity, invexity, and invex monotonicity re- quired in our study; in Sections 3 and 4, we introduce the new class of generalized invex monotone plus mappings, and generalized invex cocoercive mappings ...
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Symmetric Duality for Bonvex Multiobjective Fractional Continuous Time Programming Problems
... ∫ } is linearly independent. If The invexity conditions of Theorem 3.1 are satisfied , then (x 0 (t),y 0 (t),l 0 , λ 0 ) is properly efficient for (MFP*) In order to present a better view of the concept of second ...
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Global Optimisation for Energy System
... The conditions for KT-invexity that exist in the literature take these relations into account but, to the best of our knowledge, do not provide any clear procedure for identifying KT- invex problems. Therefore, ...
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Vol 2, No 9 (2011)
... N otions of invexity as function and as set are generalized. The pre–invex functions with respect to η (without differentiability) have been generalized. In this paper, the class of pre–invex functions introduced ...
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