arXiv subjects

Kuntal Som

Publications and source records attributed to Kuntal Som.

3 recordsLinked to original sources

arXiv2025

Remarks on the paper "Treatment of Set-Valued Robustness via Separation and Scalarization"

In this paper, we remark on the published paper "Treatment of Set-Valued Robustness via Separation and Scalarization" [1], which deals with the robust solution to an uncertain constrained set-valued optimization problem via scalarization methods. We show many inconsistencies in the results of the above-mentioned paper. We improve most of these results. In the process, we introduce some new concepts of robust solutions for uncertain set-valued optimization problems. We also improve some results on scalarization methods applicable to set-valued optimization.

math.OC↗

arXiv2025

Bilevel Programming Problems: A view through Set-valued Optimization

Bilevel programming is one of the very active areas of research with many real-life applications in economics and engineering. Bilevel problems are hierarchical problems consisting of lower-level and upper-level problems, respectively. The leader or the decision-maker for the upper-level problem decides first, and then the follower or the lower-level decision-maker chooses his/her strategy. In the case of multiple lower-level solutions, the bilevel problems are not well defined, and there are many ways to handle such a situation. One standard way is to put restrictions on the lower level problems (like strict convexity) so that nonuniqueness does not arise. However, those restrictions are not viable in many situations. Therefore, there are two standard formulations, called pessimistic formulations and optimistic formulations of the upper-level problem. A set-valued formulation has been proposed and has been studied in the literature. However, the study is limited to the continuous set-up with the assumption of value attainment, and the general case has not been considered. In this paper, we focus on the general case and study the connection among various notions of solution. Our main findings suggest that the set-valued formulation may not hold any bigger advantage than the existing optimistic and pessimistic formulation.

math.OC↗

arXiv2025

Zero-Error Nash Equilibrium: Harnessing Nonlocal Correlation in Incomplete Information Games

Claude Shannon's zero-error communication paradigm reshaped our understanding of fault-tolerant information transfer. Here, we adapt this notion into game theory with incomplete information. We ask: can players with private information coordinate on a Nash equilibrium with zero probability of error? We identify Bayesian games in which such coordination is impossible classically, yet achievable by harnessing Bell nonlocal correlations. We formalize this requirement as zero-error Nash equilibrium coordination, establishing a new bridge between information theory, game theory, and quantum nonlocality. Furthermore, we construct a tripartite Bayesian game that admits zero-error Nash equilibrium coordination with genuine entanglement, and a two-player game where a stronger notion of coordination can be achieved using every two-qubit pure entangled state except the maximally one. Crucially, the advantage persists under experimentally relevant noise, demonstrating nonlocality as a robust resource for near-zero error decision-making under uncertainty.

quant-ph↗