Using Ellipsoids in Weighted Projective Algorithms for Nondifferentiable Optimization
We show how to modify the method of Goffin et al. (1992) and how to implement it efficiently for nondifferentiable convex minimization (NDCM). It is an application of a variant of an interior point algorithm to a cutting planes method for the minimizing function defined by supporting hyperplanes to its epigraph. In both algorithms new supporting hyperplanes are generated in weighted analytic centers (WAC) of certain polytope containing feasible set. A special ellipsoid centered in WAC is constructed to eliminate inactive supporting hyperplanes.
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