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Seminar & Colloquium

Seminar & Colloquium 게시글의 상세 화면
제목 [2018/05/24] Dr. Juyoung Jeong (UMBC)
작성자 관리자 등록일 2018-05-17 조회수 80

Speaker:  Dr. Juyoung Jeong (UMBC)

Date: May 24. Thursday 14:00 - 15:00

Room: AORC Seminar Room (General Studies, 기초학문관 3층)

Title: Permutation invariant proper polyhedral cones and their Lyapunov rank

 
Abstract:
 
The Lyapunov rank  of a proper cone K in a finite dimensional real Hilbert space 
is defined as the dimension of the space of all Lyapunov-like transformations on K. This rank measures the number of linearly independent bilinear relations needed to express a complementarity system on K (that arises, for example, from a linear program or a complementarity problem on the cone). 
Motivated by the problem of describing  spectral/proper cones where the complementarity system can be expressed as a square system (that is, where the  Lyapunov rank is greater than equal to the dimension of the ambient space), we consider proper polyhedral cones in R^n that are permutation invariant. For such cones we show that the Lyapunov rank is either 1 (in which case, the cone is irreducible) or n (in which case, the cone is isomorphic to the nonnegative orthant in R^n). 
In the latter case, we show that the corresponding  spectral cone is isomorphic to a symmetric cone.
Seminar & Colloquium 게시판의 이전글 다음글
이전글 [2018/05/25] Prof. Kyu-Hwan Lee (Department of Mathematics, University of Connecticut)
다음글 Seminars and Talks of this week (May 14~18, 2018)
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