2024/08/29 by Sina Arefizadeh, Arefizadeh, Sina, Angelia Nedich +1 · 2 citations
Computer Science · Engineering · #Assembly Line Balancing Optimization #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Mechanical stress and fatigue analysis #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.2408.16918
openalex publication_date 2024/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we focus on deriving some sufficient conditions for the existence of solutions to non-monotone Variational Inequalities (VIs) based on inverse mapping theory. We have obtained several widely applicable sufficient conditions for this problem and have introduced a sufficient condition for the existence of a Minty solution. We have shown that the extra-gradient method converges to a solution of VI in the presence of a Minty solution. Additionally, we have shown that, under some extra assumption, the algorithm is efficient and approaches a particular type of Minty solution. Interpreting these results in an equivalent game theory problem, weak coupling conditions will be obtained, stating that if the players' cost functions are sufficiently weakly coupled, the game has a pure quasi-Nash equilibrium. Moreover, under the additional assumption of the existence of Minty solutions, a pure Nash equilibrium exists for the corresponding game.