Dr Vivek Singh
@iitism.ac.in
Department of Applied Mathematics
Indian School of Mines, Dhanbad
Scopus Publications
Scholar Citations
Scholar h-index
Scopus Publications
Vivek Singh, Neelima Shekhawat, and M. K. Dubey
AIP Publishing
Mallika Dhingra, M. K. Dubey, Vivek Singh, and Anand P. Singh
AIP Publishing
Vivek Singh, Shivesh Kishore Karan, Chandrakant Singh, and Sukha Ranjan Samadder
Springer Science and Business Media LLC
Vivek Singh, I. Ahmad, S.K. Gupta, and S. Al-Homidan
National Library of Serbia
The purpose of this article is to introduce the concept of second order (?,?)-invex function for continuous case and apply it to discuss the duality relations for a class of multiobjective variational problem. Weak, strong and strict duality theorems are obtained in order to relate efficient solutions of the primal problem and its second order Mond-Weir type multiobjective variational dual problem using aforesaid assumption. A non-trivial example is also exemplified to show the presence of the proposed class of a function.
Vivek Singh, Anurag Jayswal, S. Al-Homidan, and I. Ahmad
World Scientific Pub Co Pte Lt
In this paper, we present a new class of higher order [Formula: see text]-[Formula: see text]-invex functions over cones. Further, we formulate two types of higher order dual models for a vector optimization problem over cones containing support functions in objectives as well as in constraints and establish several duality results, viz., weak and strong duality results.
Anurag Jayswal and Vivek Singh
Springer Science and Business Media LLC
In this article, we focus to study about modified objective function approach for multiobjective optimization problem with vanishing constraints. An equivalent η-approximated multiobjective optimization problem is constructed by a modification of the objective function in the original considered optimization problem. Furthermore, we discuss saddle point criteria for the aforesaid problem. Moreover, we present some examples to verify the established results.
Shivesh Kishore Karan, Sukha Ranjan Samadder, and Vivek Singh
Wiley
Extensive coal mining results in ecological upheaval. Mining activities such as excavation and dumping of overburden convert land into new habitats, which completely degrades the soil structure. Adverse impacts of coal mining activities on water resources have been reported from several such regions. This study focusses on the assessment of groundwater vulnerability due to land degradation in coal mining areas. Three techniques were used to study the groundwater vulnerability: (a) the original DRASTIC overlay and index based model, (b) a modified DRASTIC model developed by adding land use and distance from lineament parameters, and (c) a model developed using analytic hierarchy process to optimise the rates and weights of the modified DRASTIC parameters. The groundwater vulnerability assessment models were validated by comparing the analysed groundwater samples data of the region and then by comparing with the computed overall water quality index for each sampling site. The results showed that groundwater vulnerability assessment in coal mining areas can be significantly improved. The best results were observed using an analytic hierarchy process–Modified DRASTIC model, which showed the highest positive significant (p < .01) correlation (r = .94) with the water quality index. Spatial distribution results revealed critical impact of land degradation due to coal mining on groundwater, as nearly 24% of the entire study area lied in the high to very high vulnerable zones, most of which are located in the vicinity of mining areas. This study will help in better water management practices in coal mining areas.
Anurag Jayswal, Vivek Singh, and Krishna Kummari
Springer Science and Business Media LLC
Abstract In this paper, we present new class of higher-order $$(C, \\alpha , \\rho , d)$$(C,α,ρ,d)-convexity and formulate two types of higher-order duality for a nondifferentiable minimax fractional programming problem. Based on the higher-order $$(C, \\alpha , \\rho , d)$$(C,α,ρ,d)-convexity, we establish appropriate higher-order duality results. These results extend several known results to a wider class of programs.
I. Ahmad, Krishna Kummari, Vivek Singh, and Anurag Jayswal
National Library of Serbia
The aim of this work is to study optimality conditions for nonsmooth minimax programming problems involving locally Lipschitz functions by means of the idea of convexifactors that has been used in [J. Dutta, S. Chandra, Convexifactors, generalized convexity and vector optimization, Optimization, 53 (2004) 77-94]. Further, using the concept of optimality conditions, Mond-Weir and Wolfe type duality theory has been developed for such a minimax programming problem. The results in this paper extend the corresponding results obtained using the generalized Clarke subdifferential in the literature.
Anurag Jayswal, Vivek Singh, and I. Ahmad
Inderscience Publishers
Anurag Jayswal, Krishna Kummari, and Vivek Singh
National Library of Serbia
As duality is an important and interesting feature of optimization problems, in this paper, we continue the effort of Long and Huang [X. J. Long, N. J. Huang, Optimality conditions for efficiency on nonsmooth multiobjective programming problems, Taiwanese J. Math., 18 (2014) 687-699] to discuss duality results of two types of dual models for a nonsmooth multiobjective programming problem using convexificators.
Anurag Jayswal, Krishna Kummari, and Vivek Singh
FapUNIFESP (SciELO)
The Karush-Kuhn-Tucker type necessary optimality conditions are given for the nonsmooth minimax fractional programming problem with inequality and equality constraints. Subsequently, based on the idea of L-invex-infine functions defined in terms of the limiting/Mordukhovich subdifferential of locally Lipschitz functions, we obtain sufficient optimality conditions for the considered nonsmooth minimax fractional programming problem and also we provide an example to justify the existence of sufficient optimality conditions. Furthermore, we propose a parametric type dual problem and explore duality results.