joint work with Narin Petrot
We introduce generalized forward–backward splitting methods with penalty terms for solving monotone inclusion problems involving the sum of a finite number of maximally monotone operators and the normal cone to the nonempty set of zeros of another maximally monotone operator. We show convergences of the iterates, provided that the condition corresponding to the Fitzpatrick function of the operator describing the set of the normal cone is fulfilled. We illustrate the functionality of the methods through some numerical experiments
joint work with Radu Boţ, Robert Ernö Csetnek
We propose a proximal algorithm for minimizing objective functions consisting of three summands: the composition of a nonsmooth function with a linear operator, another nonsmooth function and a smooth function which couples the two block variables. The algorithm is a full splitting method. We provide conditions for boundedness of the sequence and prove that any cluster point is a KKT point of the minimization problem. In the setting of the Kurdyka-Lojasiewicz property, we show global convergence and derive converge rates for the iterates in terms of the Lojasiewicz exponent.
joint work with Christof Büskens
Mehrotra's predictor-corrector method for linear and convex quadratic programming is well known for its great practical performance. Strictly speaking it does lack a convergence theory however. As a result, there are examples for which Mehrotra-type algorithms fail to converge. In the talk, divergence on particularly small quadratic programs is examined. Different strategies and safe guards for promoting convergence are discussed.