In this talk, we will present a framework for analyzing, in the high-dimensional limit, the exact dynamics of several stochastic optimization algorithms that arise in signal and information processing. For concreteness, we consider two prototypical problems: sparse principal component analysis and regularized linear regression (e.g. LASSO). For each case, we show that the time-varying estimates given by the algorithms will converge weakly to a deterministic “limiting process” in the high-dimensional (scaling and mean-field) limit. Moreover, this limiting process can be characterized as the unique solution of a nonlinear PDE, and it provides exact information regarding the asymptotic performance of the algorithms. For example, performance metrics such as the MSE, the cosine similarity and the misclassification rate in sparse support recovery can all be obtained by examining the deterministic limiting process. A steady-state analysis of the nonlinear PDE also reveals interesting phase transition phenomena related to the performance of the algorithms. Although our analysis is asymptotic in nature, numerical simulations show that the theoretical predictions are accurate for moderate signal dimensions.