The interior point method for nondifferentiable optimization
General nondifferentiable convex minimization problems with box constraints are considered. Modern ideas of the problem solution are discussed. This is suggested to construct a piecewise linear approximation from below for the minimized function (the method of cutting planes). To find a cutting plane (support hyperplane), interior point methods are of use. These methods are divided into two groups: the potential function (Karmarkar's) method and the analytical center (trajectory) method, which are generalized by introduction of weighes. Duality of the methods is demonstrated. The weighted analytical center algorithm is presented in the paper. To eliminate inactive cutting planes, the ellipsoid method is accepted. Three methods are considered to restore the admissibility after the number of hyperplanes in the function approximation is decreased. The methods are investigated numerically. The general scheme of a nondifferentiable convex minimization algorithm with exclusion is given. The scheme is tested for the aforesaid variants of the method. Four standard testing examples are used and thorough research (10 tables) is fulfilled.
scientific article; zbMATH DE number 880849