The high computational cost (CC) of neuromusculoskeletal modeling is usually considered a serious barrier in clinical applications. Different approaches have been developed to lessen CC and amplify the accuracy of muscle activation prediction based on forward and inverse analyses by applying different optimization algorithms. This study is aimed at proposing two novel approaches, inverse muscular dynamics with inequality constraints (IMDIC) and inverse-forward muscular dynamics with inequality constraints (IFMDIC), not only to reduce CC but also to amend the computational errors compared to the well-known approach of extended inverse dynamics (EID). To do that, the equality constraints of optimization problem, which are computationally tough to satisfy, are replaced by inequality constraints, which are easier to satisfy. To verify the practical application of the proposed approaches, the muscle activations of the lower limbs during the half of a gait cycle are quantified. The simulation results of the optimal muscle activations are then compared to the experimental ones. The results reveal that IMDIC requires less CC (87.5%) compared to EID. In addition, CC of IMDIC was about 33.3% improved by the application of IFMDIC. The findings of this study suggest that although the novel approach of IFMDIC decreases CC compared to IMDIC, the convergence of its results is very sensitive to the primary guess of the optimization variables.