In this paper, we investigate the multiple access spatial modulation (MASM) in multiple-input multiple-output (MIMO) systems with the aid of dual-ascent inspired iterative transmit precoding (TPC) methods. To find a global optimum against the maximum minimum Euclidean distance (MMD) problem, as well as to reach a fast convergence rate with low-complexity, we first study the peculiarities of the convex optimization methods that take the dual- ascent method into account. This beneficially provides us an insight into developing a new dual- ascent method which is capable of bringing robustness to the existing dual-ascent method. Then, we introduce an evolving MASM-MIMO system by imposing non-stationary time-varying TPC parameters, and thereby resulting in a guaranteed Euclidean distance (GED) aided TPC method. Numerical results reveal that our proposals are capable of promoting a significant bit error rate (BER) performance improvement comparing with the existing methods for the MASM-MIMO systems, as well as facilitating a fast convergence with low- complexity.