A self-driving vehicle is required to perform all lane merge scenarios when performing lane change/merge functions during its autonomous mode. Most challenging of such merge scenarios is the highway merge from a local lane to the highway lane. This is compounded when there is no acceleration or surplus road to implement the merge from the merge lane to highway lane.This paper presents a Model Predictive Control (MPC) based optimal control strategy to solve the merge problem for autonomous vehicle performing this merge. A kinematic model is used to predict the merge vehicle states. This model is then used to solve an optimal highway merge problem without an acceleration areafor the merge vehicle subjected to various constraints. Simulation results are presented that show that the show the merge maneuver being implemented.