Browsing by Author "Avanish Shahi"

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On geodesic convex and generalized geodesic convex functions over Riemannian manifolds
(American Institute of Physics Inc., 2018) Avanish Shahi; S.K. Mishra
In this paper, we have obtained geodesic convex and geodesic pseudoconvex functions from the ratio of the square of a non-negative geodesic convex to a strictly positive geodesic concave; and by the ratio of a geodesic convex and related functions to a positive affine and some generalized convex functions, respectively, over Riemannian manifolds. Further, we have proved that the ratio of a non-negative geodesic convex to a positive geodesic concave function is a geodesic quasiconvex function. © 2018 Author(s).
On Monotone Maps: Semidifferentiable Case
(Springer Verlag, 2020) Shashi Kant Mishra; Sanjeev Kumar Singh; Avanish Shahi
In this paper, we define the concepts of monotonicity and generalized monotonicity for semidifferentiable maps. Further, we present the characterizations of convexity and generalized convexity in case of semidifferentiable functions. These results rely on general mean-value theorem for semidifferentiable functions (J Glob Optim 40:503–508, 2010). © 2020, Springer Nature Switzerland AG.
On semidifferentiable interval-valued programming problems
(Springer Science and Business Media Deutschland GmbH, 2021) Kin Keung Lai; Avanish Shahi; Shashi Kant Mishra
In this paper, we consider the semidifferentiable case of an interval-valued minimization problem and establish sufficient optimality conditions and Wolfe type as well as Mond–Weir type duality theorems under semilocal E-preinvex functions. Furthermore, we present saddle-point optimality criteria to relate an optimal solution of the semidifferentiable interval-valued programming problem and a saddle point of the Lagrangian function. © 2021, The Author(s).
On strong pseudomonotone and strong quasimonotone maps
(Springer New York LLC, 2018) Sanjeev Kumar Singh; Avanish Shahi; S.K. Mishra
We introduce strong pseudomonotone and strong quasimonotone maps of higher order and establish their relationships with strong pseudoconvexity and strong quasiconvexity of higher order, respectively, which yields first-order characterizations of strong pseudoconvex and strong quasiconvex functions of higher order. Moreover, we answer the open problem (converse part of Proposition 6.2) of Karamardian and Schaible (J. Optim. Theory Appl. 66:37–46,1990), for even more generalized functions, namely strongly pseudoconvex functions of higher order. © Springer Nature Singapore Pte Ltd. 2018.
Optimality and Duality of Pseudolinear Multiobjective Mathematical Programs with Vanishing Constraints
(Springer Science and Business Media Deutschland GmbH, 2021) Jitendra Kumar Maurya; Avanish Shahi; Shashi Kant Mishra
In this chapter, we establish necessary and sufficient optimality conditions for a special class of optimization problems called multiobjective mathematical programs with vanishing constraints under pseudolinear assumption. We propose Mond–Weir type dual model for the considered problem and establish usual duality results. Furthermore, we present some examples to validate our results. © 2021, Springer Nature Switzerland AG.
Properties of geodesic semilocal E-B-preinvex functions and applications in multiobjective fractional programming problems
(International Publications, 2019) Avanish Shahi; S.K. Mishra
In this paper, we introduce the concept of geodesic semilocal E-B-preinvex functions on Riemannian manifolds and discuss some of its properties. Further, we establish sufficient optimality conditions and duality theorems for nonlinear multiobjective fractional programming problems. © 2019, International Publications. All rights reserved.
Pseudoinvex functions on riemannian manifolds and applications in fractional programming problems
(Politechnica University of Bucharest, 2018) Avanish Shahi; S.K. Mishra
In this paper, we have obtained pseudoinvex functions from the ratio of invex and related functions to an affine and some generalized invex functions on Riemannian manifolds. Further, we establish sufficient optimality conditions and duality theorems for fractional nonlinear optimization problems under weaker assumptions on Riemannian manifolds. © 2018 UPB Scientific Bulletin, Series A: Applied Mathematics and Physics. All rights reserved.
Strong Pseudoconvexity and Strong Quasiconvexity of Non-differentiable Functions
(Springer Science and Business Media Deutschland GmbH, 2021) Sanjeev Kumar Singh; Avanish Shahi; Shashi Kant Mishra
In this chapter, we introduce the concept of strong pseudomonotonicity and strong quasimonotonicity of set-valued maps of higher order. Non-differentiable strong pseudoconvex/quasiconvex functions of higher order are characterized by the strong pseudomonotonicity/quasimonotonicity of their corresponding set-valued maps. As a by-product, we solve the open problem (converse part of Proposition 6.2) of Karamardian and Schaible (J. Optim. Theory Appl. 66:37–46, 1990) for the more general case as strong pseudoconvexity for non-smooth, locally Lipschitz continuous functions. © 2021, Springer Nature Switzerland AG.