Frank-Wolfe algorithm

The Frank–Wolfe algorithm is an iterative first-order optimization algorithm for constrained convex optimization. Also known as the conditional gradient method,reduced gradient algorithm and the convex combination algorithm, the method was originally proposed by Marguerite Frank and Philip Wolfe in 1956. In each iteration, the Frank–Wolfe algorithm considers a linear approximation of the objective function, and moves towards a minimizer of this linear function (taken over the same domain).

Suppose ${\displaystyle {\mathcal {D}}}$ is a compact convex set in a vector space and ${\displaystyle f\colon {\mathcal {D}}\to \mathbb {R} }$ is a convex differentiable real-valued function. The Frank–Wolfe algorithm solves the optimization problem

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