In this article, we investigate the utilization of the restricted Bayesian lasso regression, focusing on high-dimensional models that incorporate linear inequality constraints on the coefficients. The lasso technique, recognized for its effectiveness in variable selection and regularization, is further refined by embedding a Bayesian framework that integrates prior knowledge and addresses uncertainty in coefficient estimates. We examine subspace inequality constraints and outline the theoretical foundations of the restricted Bayesian lasso, including the formulation of prior distributions and the computational methods used to obtain posterior distributions. Through simulation studies and real-world data applications, we aim to illustrate the advantages of this methodology compared to traditional Bayesian lasso regression, with particular emphasis on enhancements in estimation accuracy, prediction performance, and variable selection efficiency.

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