Global Conference on Mathematics and Applications (GCMA)

This work focuses on unconstrained multi-objective optimization problems, where the presence of several objectives generally prevents the existence of a unique minimizer. Consequently, the classical zero-gradient condition is replaced by the concept of Pareto stationarity for the vector-valued objective function. The authors propose a gradient-based descent framework that generates a common descent direction for all objective functions while satisfying a sufficient decrease condition analogous to the standard Wolfe line-search conditions. Furthermore, global convergence to a Pareto-stationary point is established without imposing any convexity assumptions.