Browsing by Author "Pankaj"

Now showing 1 - 7 of 7
  • Thumbnail Image
    Publication
    E-convex functions and nonsmooth mathematical programs
    (International Publications, 2021) Joshi, Bhuwan Chandra; Mohan, Rakesh; Pankaj
    In this paper, we derive sufficient optimality condition for a nonsmooth mathematical program with equilibrium constraints using E-convex functions. We formulate the Wolfe and Mond-Weir type duality models and establish weak and strong duality theorems to relate the mathematical program with equilibrium constraints and the dual models in the framework of convexificators. � 2021, International Publications. All rights reserved.
  • Thumbnail Image
    Publication
    Future Prospects of Biodegradable Polymers with Potential Application in Food Industry
    (Springer Nature, 2022) Patil, Tejaswini; Tripathi, Abhishek Dutt; Rai, Dinesh Chandra; Agarwal, Aparna; Paul, Veena; Maurya, Kamlesh Kumar; Pankaj
    Enormous plastic production and its consumption and accumulation are a global concern. Although the solution to this issue is �reuse, recycle, and reduce plastic, " it is not quite enough, and therefore biodegradable packaging material is gaining acceptability in the agriculture and food industry for packaging purposes. This chapter summarizes recent approaches and innovations in the field of biodegradable polymers and future prospects. Here, biodegradable polymers and natural polymers with their properties, their applicability, and their degradation are discussed. Also, improvements in properties of natural polymers by using technologies have been discussed. Biodegradable polymers reduce the burden of greenhouse gases on Earth. � The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022.
  • Thumbnail Image
    Publication
    GENERALIZED INVEXITY and MATHEMATICAL PROGRAMS
    (Faculty of Organizational Sciences, Belgrade, 2021) Joshi, Bhuwan Chandra; Mohan, Rakesh; Pankaj
    In this paper, using generalized convexity assumptions, we show that M-stationary condition is sufficient for global or local optimality under some mathematical programming problem with equilibrium constraints(MPEC). Further, we formulate and study Wolfe type and Mond-Weir type dual models for the MPEC, and we establish weak and strong duality theorems. � 2021 Faculty of Organizational Sciences, Belgrade. All rights reserved.
  • Thumbnail Image
    Publication
    Introduction: Scope and Importance of Biodegradable Polymers
    (Springer Nature, 2022) Paul, Veena; Tripathi, Abhishek Dutt; Maurya, Kamlesh Kumar; Pankaj; Dinesh; Rai, Dinesh Chandra
    In today�s world, the interest in biodegradable polymers has grown significantly. The demand for these polymers has skyrocketed, making them broadly utilized polymers with a range of several applications. Plant, animal, and microbially derived biopolymers have piqued the interest of researchers. Because of their inherent properties like biodegradability, biocompatibility, inexhaustibility, and economic availability, the need for biodegradable polymers has been enhanced. Recent trends in the food packaging industry have shown the employment of biodegradable polymers with improved characteristics. This chapter emphasizes biodegradable polymers� development, classification, application, challenges, and market opportunities. The application of these polymers in active and intelligent packaging are summarized. This chapter also highlights the application of biodegradable polymers as an assuring green technique for assuring the quality and safety of food. � The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022.
  • Thumbnail Image
    Publication
    Mathematical programs involving e-convex functions
    (Politechnica University of Bucharest, 2021) Joshi, Bhuwan Chandra; Pankaj
    In this paper, we have shown that generalized M-stationary condition is sufficient for global optimality under the assumptions of E-convexity and mathematical programming problems with equilibrium constraints. Further, we formulate and study Wolfe type and Mond-Weir type dual models for the MPEC and we establish weak and strong duality theorems relating to the MPEC and the two dual models. � 2021, Politechnica University of Bucharest. All rights reserved.
  • Thumbnail Image
    Item
    Optimality and duality results for fractional programming problems under E-univexity
    (Springer, 2024) Mishra S.K.; Singh D.; Pankaj
    In this article, we deal with nonconvex fractional programming problems involving E-differentiable functions (FPE). The so-called E-Karush-Kuhn-Tucker sufficient E-optimality conditions are established for nonsmooth optimization problems under E-univexity hypothesis. The established optimality conditions are explained with a numerical example. The so-called vector dual problem in the sense of Schaible (SDE) involves E-differentiable functions for (FPE) is defined under E-univexity hypothesis. � The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.
  • Thumbnail Image
    Publication
    Vector Variational Inequalities in Terms of Fr�chet Subdifferentials with Genralized Convex Function
    (International Publications, 2022) Joshi, Bhuwan Chandra; Mohan, Rakesh; Pankaj
    In this paper,nonsmooth vector optimization problem involving approximate starshaped preinvex functions and strongly locally starshaped invex functions in terms of the Fr�chet subdifferentials is considered. Further, we derive optimality conditions for a point to be a local sharp and local weak sharp efficient solution of the vector optimization problem involving approximately starshaped preinvex and strongly locally starshaped invex functions in terms of the Fr�chet subdifferentials and superdifferentials. In order to justify the theorems some examples are also given. � 2022, International Publications. All rights reserved.