arXiv subjects

Soumitra Dey

Publications and source records attributed to Soumitra Dey.

7 recordsLinked to original sources

arXiv2026

Multi-split Multiple-sets Implicit Convex Feasibility Seeking As Split Inverse Problems

We introduce a new class of problems, termed multi-split multiple-sets implicit convex feasibility problems (MSMS-ICFPs), define a proximity function for it and analyze its properties under certain assumptions on the involved general point-to-set operators. Additionally, we discuss its properties for a special class of point-to-set operators. For these kinds of point-to-set operators, we deploy a new iterative algorithm to solve the associated MSMS-ICFP and show that any sequence generated by it converges in norm to a solution of the MSMS-ICFP whenever a solution exists (i.e., in the consistent case). We also define a generalized proximity function for the MSMS-ICFP using the Bregman distance. Based on this function, we present a generalized simultaneous projection gradient algorithm for the split feasibility problem with multiple output sets, by examining various related results. We conclude by discussing several further special cases of the MSMS-ICFP.

math.OC↗

arXiv2026

String-averaging bargaining in solidarity cooperative games

We consider the situation that the grand set of all players, in a cooperative game in characteristic function form with a nonempty core, consists of recognizable subsets of players. The underlying assumption is that the players of each subset have something in common between themselves which is not shared by the players of other subsets. For example, the members of these subsets are distinguishable by their nationalities or by their geographic locations or by some other market-related economic or social property. In addition to the agreement of all players to play the game to reach a point in the core, the members of each subset want to steer the iterative orbit of the bargaining process to a point in the core that will reflect the strength of their solidarity within their subset. This is why we call such subsets solidarity sets. The solidarity means that players of a solidarity set are willing to participate in coalitions that include only members of their solidarity set and are not willing to participate in coalitions of other solidarity sets. The question is how can such a game be played? Is there an iterative bargaining scheme that will generate a sequence of payoffs that converges to a point in the core which reflects the solidarity of the members of the solidarity sets? We propose bargaining schemes that allow the members of each solidarity set to perform, independently from other solidarity sets and, therefore, simultaneously in time, a full but finite sweep of intercoalitional collaboration. Then the end-points of all these sweeps are combined into a single payoff vector via a convex combination wherein the coefficients of the convex combination may reflect some a priori knowledge about the relative strengths of the different solidarity sets. These bargaining schemes are applied to a new type of cooperative game that we call solidarity cooperative game (SCG).

math.OC↗

arXiv2023

Levitin-Polyak well-posedness of split multivalued variational inequalities

We introduce and study the split multivalued variational inequality problem (SMVIP) and the parametric SMVIP. We examine, in particular, Levitin-Polyak well-posedness of SMVIPs and parametric SMVIPs in Hilbert spaces. We provide several examples to illustrate our theoretical results. We also discuss several important special cases.

math.OC↗

arXiv2023

New iterative algorithms for solving split variational inclusions

In this paper we study a class of split variational inclusion (SVI) and regularized split variational inclusion (RSVI) problems in real Hilbert spaces. We discuss various analytical properties of the net generated by the RSVI and establish the existence and uniqueness of the solution to the RSVI. Using analytical properties of this net and under certain assumptions on the parameters and mappings associated with the SVI, we establish the strong convergence of the sequence generated by our proposed iterative algorithm. We also deduce another iterative algorithm by taking the regularization parameters to be zero in our proposed algorithm. We establish the weak convergence of the sequence generated by our new algorithm under certain assumptions. Moreover, we discuss two special cases of the SVI, namely the split convex minimization and the split variational inequality problems, and give several numerical examples.

math.OC↗

arXiv2023

Well-posedness for the split equilibrium problem

We extend the concept of well-posedness to the split equilibrium problem and establish Furi-Vignoli-type characterizations for the well-posedness. We prove that the well-posedness of the split equilibrium problem is equivalent to the existence and uniqueness of its solution under certain assumptions on the bifunctions involved. We also characterize the generalized well-posedness of the split equilibrium problem via the Kuratowski measure of noncompactness. We illustrate our theoretical results by several examples.

math.OC↗

arXiv2023

Levitin-Polyak Well-posedness for Split Equilibrium Problems

The notion of well-posedness has drawn the attention of many researchers in the field of nonlinear analysis, as it allows to explore problems in which exact solutions are not known and/or computationally hard to compute. Roughly speaking, for a given problem, well-posedness guarantees the convergence of approximations to exact solutions via an iterative method. Thus, in this paper we extend the concept of Levitin-Polyak well-posedness to split equilibrium problems in real Banach spaces. In particular, we establish a metric characterization of Levitin-Polyak well-posedness by perturbations and also show an equivalence between Levitin-Polyak well-posedness by perturbations for split equilibrium problems and the existence and uniqueness of their solutions.

math.OC↗

arXiv2022

A Neural Network for Solving Inverse Quasi-Variational Inequalities

We study the existence and uniqueness of solutions to the inverse quasi-variational inequality problem. Motivated by the neural network approach to solving optimization problems such as variational inequality, monotone inclusion, and inverse variational problems, we consider a neural network associated with the inverse quasi-variational inequality problem, and establish the existence and uniqueness of a solution to the proposed network. We prove that every trajectory of the proposed neural network converges to the unique solution of the inverse quasi-variational inequality problem and that the network is globally asymptotically stable at its equilibrium point. We also prove that if the function which governs the inverse quasi-variational inequality problem is strongly monotone and Lipschitz continuous, then the network is globally exponentially stable at its equilibrium point. We discretize the network and show that the sequence generated by the discretization of the network converges strongly to a solution of the inverse quasi-variational inequality problem under certain assumptions on the parameters involved. Finally, we provide numerical examples to support and illustrate our theoretical results.

math.OC↗