  Vector optimization problems are a generalization of multiobjective
optimization in which the preference order is related to an arbitrary closed
and convex cone, rather than the nonnegative octant. Due to its real life
applications, it is important to have practical solution approaches for
computing. In this work, we consider the inexact projected gradient-like method
for solving smooth constrained vector optimization problems. Basically, we
prove global convergence of any sequence produced by the method to a stationary
point assuming that the objective function of the problem is $K$-quasiconvex,
instead of the stronger $K$-convexity assumed in the literature.
