An interior point method for constrained saddle point problems

We present an algorithm for the constrained saddle point problem with a convex-concave function L and convex sets with nonempty interior. The method consists of moving away from the current iterate by choosing certain perturbed vectors. The values of gradients of L at these vectors provide an appropriate direction. Bregman functions allow us to define a curve which starts at the current iterate with this direction, and is fully contained in the interior of the feasible set. The next iterate is obtained by moving along such a curve with a certain step size. We establish convergence to a solutio...

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