The Corvinus Centre for Operations Research (CCOR), the Corvinus Institute for Advanced Studies (CIAS), and the Institute of Operations and Decision Sciences invite you to the minicourse by Professor Goran Lešaja (Georgia Southern University),
Kernel-Based Interior-Point Methods for Cartesian 𝒫*(κ)– Linear Complementarity Problems over Symmetric Cones
Venue: Corvinus University, Building C, Room C.7.714
Date: February 22. (Thursday) 13:00-14:00
We would like to inform you that the lectures will be broadcast online. Please be aware that this broadcast will not utilize professional-grade equipment, and we appreciate your understanding that we cannot ensure the broadcast’s quality.
If you would like to join online, please send an e-mail to anita dot varga at uni-corvinus dot hu by February 22, 8:00.
Abstract
Linear Complementarity Problems (LCP) is an important class of problems closely related to many optimization problems. Thus, efficient algorithms for solving LCPs are of the interest for theoretical and practical purposes. The main achievement of feasible Interior-Point Methods (IPMs) based on the class of eligible kernel functions for 𝒫*(κ)– LCPs over nonnegative orthant is the improved iteration bounds of long-step methods.
We consider a generalization of kernel-based IPMs to Cartesian 𝒫*(κ)– LCPs over symmetric cones. .A remarkable and surprising result has been shown relatively recently: The algebraic structures of Euclidean Jordan Algebras (EJA) and associated symmetric cones are connected to important optimization problems and can serve as a unifying frame to analyze IPMs for semi definite optimization problems, second order cone optimization problems, and classical optimization problems over nonnegative orthant. Using tools of EJA and symmetric cones it is shown that the generalization of the kernel-based IPMs for Cartesian 𝒫*(κ)-LCP over symmetric cones still match the best known iteration bounds achieved for the kernel-based IPMs for 𝒫*(κ)– LCPs over nonnegative orthant.