Mansi Dhingra

Well-setness and scalarization in set optimization

In this paper, we consider a notion of global well-setness for a set optimization problem using the excess function. We give sufficient conditions for well-setness and establish Dontchev–Zolezzi type measure for well-setness. Moreover, we relate this notion with well-setness notion for a scalar problem obtained by using generalized Gerstewitz’s function.

Pointwise and global well-posedness in set optimization: a direct approach

The aim of this paper is to characterize some of the pointwise and global well-posedness notions available in literature for a set optimization problem completely by compactness or upper continuity of an appropriate minimal solution set maps. The characterizations of compactness of set-valued maps, lead directly to many characterizations for well-posedness. Sufficient conditions are also given for global well-posedness.

Optimization reformulations of the generalized Nash equilibrium problem using regularized indicator Nikaidô–Isoda function

In this paper, we extend the literature by adapting the Nikaidô–Isoda function as an indicator function termed as regularized indicator Nikaidô–Isoda function, and this is demonstrated to guarantee existence of a solution. Using this function, we present two constrained optimization reformulations of the generalized Nash equilibrium problem (GNEP for short). The first reformulation characterizes all the solutions of GNEP as global minima of the optimization problem. Later this approach is modified to obtain the second optimization reformulation whose global minima characterize the normalized Nash equilibria. Some numerical results are also included to illustrate the behaviour of the optimization reformulations.

Approximate Lagrangian duality and saddle point optimality in set optimization

In this paper, we establish approximate Lagrangian multiplier rule, Lagrangian duality and saddle point optimality for set optimization problem where the solutions are defined using set relations introduced by Kuroiwa (Kuroiwa D., The natural criteria in set-valued optimization. Surikaisekikenkyusho Kokyuroku 1031 (1998) 85–90).

Approximate solutions and scalarization in set-valued optimization

Abstract Certain notions of approximate weak efficient solutions are considered for a set-valued optimization problem based on vector and set criteria approaches. For approximate solutions based on the vector approach, a characterization is provided in terms of an extended Gerstewitz’s function. For the set approach case, two notions of approximate weak efficient solutions are introduced using a lower and an upper quasi order relations for sets and further compactness and stability aspects are discussed for these approximate solutions. Existence and scalarization using a generalized Gerstewitz’s function are also established for approximate solutions, based on the lower set order relation.

Temperature controlled junction behavior of polyaniline/ZnO heterostructures

Organic-Inorganic hybrid materials have remained an active field of research both from the point of understanding the interfaces and for device purpose. In the present work, Zinc Oxide (ZnO) - Polyaniline (PANI) interface obtained by drop casting PANI nanofibres on sputtered ZnO thin film is investigated. The study of layer by layer deposition of organic and inorganic materials to form interface, is a very important issue related to carrier transport, charge separation, structural connectivity and interfacial defects. I-V characteristics were performed for different thickness of the underlying ZnO layer. The effect of temperature on the I-V characteristics is also investigated. Hall measurements were performed to estimate the charge carrier concentration of the n-ZnO and the p-PANI. Morphology and thickness of the interface was studied using SEM imaging technique. These interfaces could be explored for different applications in areas like sensors and optoelectronics.