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math.OC2022
On the structure of the copositive cone
Roland Hildebrand, Andrey Afonin
In this work we complement the description of the extreme rays of the copositive cone with some topological structure. In a previous paper we decomposed the set of ext…
math.OC2022
Optimization in complex spaces with the Mixed Newton Method
Sergey Bakhurin, Roland Hildebrand, Mohammad Alkousa +2
We propose a second-order method for unconditional minimization of functions of complex arguments. We call it the Mixed Newton Method due to the use of the mixed Wirtinger d…
math.OC2022
Optimal step length for the maximal decrease of a self-concordant function by the Newton method
Anastasia Ivanova, Roland Hildebrand
In this paper we consider the problem of finding the optimal step length for the Newton method on the class of self-concordant functions, with the decrease in function value as cri…