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An interior point method for linear programming based on affine transformations. In the primal affine-scaling algorithm, a problem in standard form is transformed so that the current solution estimate is mapped to the point (1, 1,..., 1). A movement is then made in the transformed space in the direction of the negative projected gradient. The inverse affine transformation is applied to the resulting point, to obtain a new solution estimate in the original space. In the dual affine-scaling algorithm, similar ideas are used to solve the dual problem, with the affine trans-formations applied to the dual slack variables. Interior point methods; Nonlinear programming.