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An Application of the Frank-Wolfe Algorithm at Maximum Likelihood Estimation Problems

Ciprian Costin POPESCU


constrained maximum likelihood, nonlinear programming, Frank-Wolfe algorithm


This paper tackles the problem of maximum likelihood estimation [2] under various types of constraints (equalities and inequalities restrictions) on parameters. The initial model, which is in fact a maximization problem (here are a few methods available in literature for estimating the parameters: ERM (expectation-restricted-maximization) algorithms, GP (gradient projection) algorithms and so on) is change into a new problem, a minimization problem. This second form is suited to a variant of Frank-Wolfe method for solving linearly restricted nonlinear programming problems [5]. In this way, some difficulties from the previous approaches are removed.