Damghan University Press Analytical and Numerical Solutions for Nonlinear Equations 3060-785X 10 2 2025 12 30 Nonlinear Optimization Problems with Bipolar Fuzzy Relation Equations using Neural Networks 237 254 2032 10.22128/ansne.2025.3161.1181 EN Ali Abbasi Molai School of Mathematics and Computer Science, Damghan University, Damghan, Iran Hassan Dana Mazraeh School of Mathematics and Computer Science, Damghan University, Damghan, Iran Kourosh Parand Department of Computer and Data Sciences, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran; International Business University,Toronto, Canada Journal Article 2025 11 24 In this paper, we present a novel application of neural networks for solving nonlinear optimization problems subject to bipolar max-min fuzzy relation equation constraints. The feasible solution set for these problems is generally non-convex, which makes conventional nonlinear optimization methods less suitable for solving them. To address this challenge, we propose the use of neural networks {and some rules for simplification of the problem}. To find an input vector \( x \in [0,1]^n \) that satisfies the constraints and minimizes (or maximizes) the objective function, \( n \) neural networks are trained simultaneously. Each neural network identifies the corresponding variable of the vector \( x \in [0,1]^n \). The loss function integrates both the constraints and the objective function. Our experiments demonstrate that the proposed method can solve these problems with high accuracy and reasonable computational time. The proposed method is compared to the existing methods. https://ansne.du.ac.ir/article_2032_ada47fd9d934a1befbf960e271967e13.pdf