Bilevel optimization problems involve finding the best solution for one problem while considering another problem's optimal solution as a constraint. The goal of this study was to develop a method that ensures the upper-level solution remains feasible even with slight deviations from the optimal lower-level solution. The researchers found that by introducing the concept of near-optimality robustness, they could protect the upper-level solution from small changes in the lower-level solution. They also identified conditions for solutions to exist and proposed a solution method when the lower level is convex. Numerical results showed that exact and heuristic methods were efficient, and valid inequalities helped reduce solution time.