Generating truncated multivariate normal distributions is widely used in Bayesian constrained statistical modeling. This technique is applied in various fields, including ecology, economics, physics, computer science, biology, geosciences, and machine learning. In this paper, the efficient approach developed by [37] for generating positive Gaussian vectors is considered. Their main idea is to incorporate a smooth relaxation of the complex constraints appearing in the constrained density function into the likelihood and to employ a highly efficient Markov Chain Monte Carlo (MCMC) sampler. Our contributions are fourfold. First, we extend this approach to address linear, quadratic, and nonlinear inequality constraints, which can be applied individually or in combination. The functions generating the nonlinear inequality constraints can be piecewise continuous or continuously differentiable of any order. Second, we propose updating the approximate parameter in the likelihood at each MCMC iteration to enhance the stability and ensure the convergence of the algorithm. This allows the proposed approach to handle extreme cases that are beyond the reach of existing samplers. Third, for boundedness constraints with constant bounds, we develop an efficient formula for the log-likelihood function, which reduces computational complexity and improves efficiency in high-dimensional settings with respect to computational running time. Fourth, we explore flexibility and performance of the proposed approach through studies on both synthetic and real data within the context of Bayesian shape-restricted function estimation. A comparison with the efficient Hamiltonian Monte Carlo (HMC) sampler is included. In contrast to the HMC sampler, the starting point of the proposed MCMC does not need to satisfy the inequality constraints.