Tensor Least Angle Regression (T-LARS) is a computationally efficient method to solve large L0, or L1 constrained sparse multilinear least-squares problems for all critical values of the regularization parameter λ. The L0 and L1 are the corresponding norms of the regularization component of the sparse multilinear least square problem. In T-LARS, the optimal L1 solutions obtained during each iteration trace the trajectory of a Pareto curve. This curve contains optimal solutions to this linear or multilinear least-squares problem. We can initialize T-LARS with an L1 solution on the Pareto curve, and obtain a result with a lower residual error. However, initializing it with a solution outside the Pareto curve violates T-LARS’s optimality conditions. In this paper, we extend T-LARS using the one-dimensional L1 Homotopy method to develop the Dynamic Tensor Least Angle Regression (DT-LARS) algorithm. DT-LARS efficiently computes solutions for L1-constrained multilinear least-squares problems, even when initialized with a non-zero solution located outside the Pareto curve. Therefore, using DT-LARS, we can efficiently find a solution to a multilinear L1 least squares problem by initializing with an L1 solution from a closely related problem.