Abstract
We consider a generalized like-distance which contains as degenerate cases φ-divergences and like-distances with second order homogeneous kernel. The motivation to get this like-distance comes from studying shifted penalty functions in the primal space. These penalty functions do not necessarily have to pass through the origin with slope one and their conjugate functions allow negative values. For a particular case we get a generalization of the Kullback-Liebler entropy distance. This like-distance can be seen as the difference between a sequence of Bregman distances and their linear approximations for specific values of the arguments. Dual and primal convergence results are shown, particularly, we show that each limit point of the sequence generated by the proximal method defined by the generalized like-distance applied to the dual problem is an optimal dual solution.
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