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We develop and analyse a first-order algorithm for the A-optimal experimental design problem. The problem is first presented as a special case of a parametric family of optimal design problems for which duality results and optimality conditions are given. Then, two first-order (Frank---Wolfe type) algorithms are presented, accompanied by a detailed time-complexity analysis of the algorithms and computational results on various sized problems.

A first-order algorithm for the A-optimal experimental design problem: a mathematical programming approach