CCOR mini-course and workshop

CIAS organizes a wokshop entitled “A class of algebraically equivalent transformations for symmetric cone horizontal linear complementarity problems” with three speakers, Zsolt Darvay, Petra Renáta Rigó and Roland Török. Zsolt Darvay will also hold an introductory mini-course including three presentations in this topic.  

Mini-course 

It’s a hybrid event, you can connect online via Teams as well.  

The abstract of the mini-course: 

Analysis of the algebraically equivalent transformation technique for interior-point algorithms 

In the mini-course we present the basic concepts that are needed to introduce interior-point-algorithms based on the algebraically equivalent transformation (AET) of the central path system. First, we deal with P*(Κ)-linear complementarity problems (LCPs). We present a predictor-corrector algorithm and prove its polynomial iteration complexity. Next, we consider P*(Κ)-horizontal linear complementarity problems over the Cartesian product of symmetric cones (SCHLCPs). This includes LCPs as a special case and covers a wide range of optimization problems as well, such as semidefinite optimization and symmetric cone optimization. We propose a generalization for SCHLCPs of the predictor-corrector algorithm introduced for LCPs. Moreover, we prove that our algorithm solves the problem in polynomial time for a whole set of parameters. 

Workshop 

It’s a hybrid event, you can attend in person in room C.510, or connect online via Teams.  

13:00-13:30 

Petra Renáta Rigó: New predictor-corrector interior-point algorithm with AET function having inflection point 

We present a new predictor-corrector interior-point algorithm (PC IPA) for solving P*(Κ)-linear complementarity problems. We use the algebraically equivalent transformation (AET) technique in order to determine the search directions. In this method we apply the function φ(t)=t2−t+t√,𝜑t=t2−t+t, which has inflection point. It is interesting that the kernel corresponding to this AET function is neither self-regular, nor eligible. We show that the iteration bound of the algorithm matches the best known iteration bound for this type of PC IPAs given in the literature. 

13:30-14:00 

Roland Török: Implementation of predictor-corrector interior-point method based on a new AET fuction 

In this presentation we show numerical results about a new predictor-corrector (PC) interior-point algorithm (IPA) for solving sufficient linear complementarity problems. We applied a function having inflection point on the nonlinear equation of the central path system to define new search directions. We consider numerical results of our new method compared to other PC IPAs that use different search directions. 

14:00-14:30 Coffee break 

14:30-16:00 

Zsolt Darvay: A class of algebraically equivalent transformations for symmetric cone horizontal linear complementarity problems 

In this talk, we present a generalization of the interior-point algorithms (IPAs) introduced by Illés, Rigó, and Török [Unified approach of primal-dual interior-point algorithms for a new class of AET functions, Corvinus Econ. Work. Paper. 2022/02 (2022)]. This class of algorithms is based on the algebraically equivalent transformation (AET) of the central path system. We propose a modification of the class presented by Illés, Rigó, and Török. In the general framework of P*(Κ)-horizontal linear complementarity problems over the Cartesian product of symmetric cones, we prove the polynomial iteration complexity of the new algorithms. 

You can inquire about the possibility of connecting online at the email address marianna.eisenberg-nagy@uni-corvinus.hu. 

We encourage all interested colleagues to participate at these interesting events.