60 citations · 138 across the 20 of their papers we have counts for
28 papers
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…
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…
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…
Extremal cubics on the circle and the 2-sphere
Anastasia Ivanova, Roland Hildebrand
We study balls of homogeneous cubics on , , which are bounded by unity on the unit sphere. For we completely describe the facial structure of this nor…
Improving the constant in Nesterov's -theorem
Roland Hildebrand
One of the hard optimization problems that has a semi-definite relaxation with quantitative bound on the approximation error is the maximization of a convex quadratic form on the h…
Semi-definite representations for sets of cubics on the 2-sphere
Roland Hildebrand
The compact set of homogeneous quadratic polynomials in real variables with modulus bounded by 1 on the unit sphere is trivially semi-definite representable. The comp…