  One of the most important optimality conditions to aid to solve a vector
optimization problem is the first-order necessary optimality condition that
generalizes the Karush-Kuhn-Tucker condition. However, to obtain the sufficient
optimality conditions, it is necessary to impose additional assumptions on the
objective functions and in the constraint set. The present work is concerned
with the constrained vector quadratic fractional optimization problem. It shows
that sufficient Pareto optimality conditions and the main duality theorems can
be established without the assumption of generalized convexity in the objective
functions, by considering some assumptions on a linear combination of Hessian
matrices instead. The main aspect of this contribution is the development of
Pareto optimality conditions based on a similar second-order sufficient
condition for problems with convex constraints, without convexity assumptions
on the objective functions. These conditions might be useful to determine
termination criteria in the development of algorithms.
