A log-quadratic projection method for convex feasibility problems (Q2768005)

The convex feasibility problem which consists of finding a point in the intersection of convex sets is considered. We suggest a barycenter type projection algorithm, where the usual squared Euclidean distance is replaced by a logarithmic-quadratic distance-like functional. This allows in particular for handling efficiently feasibility problems arising in the nonnegative orthant. The proposed method includes approximate projections and is proven globally convergent under the sole assumption that the given intersection is nonempty and the errors are controllable. Furthermore, we consider the important special case involving the intersection of hyperplanes with the nonnegative orthant and show how in this case the projections can be efficiently computed via Newton's method.NEWLINENEWLINEFor the entire collection see [Zbl 0971.00058].