OPEN PROBLEMS IN THE THEORY OF COMPLETELY POSITIVE AND COPOSITIVE MATRICES

被引:47
作者
Berman, Abraham [1 ]
Duer, Mirjam [2 ]
Shaked-Monerer, Naomi [3 ]
机构
[1] Technion Israel Inst Technol, Dept Math, IL-32000 Haifa, Israel
[2] Univ Trier, Dept Math, D-54286 Trier, Germany
[3] Max Stern Yezreel Valley Coll, IL-19300 Yezreel Valley, Israel
关键词
completely positive matrices; copositive matrices; doubly nonnegative matrices; extremal matrices; copositive optimization; CP-RANK; NONNEGATIVE FACTORIZATION; SUFFICIENT CONDITIONS; TENSORS; CONE; STABILITY; FORMS; GRAPH;
D O I
10.13001/1081-3810.2943
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We describe the main open problems which are currently of interest in the theory of copositive and completely positive matrices. We give motivation as to why these questions are relevant and provide a brief description of the state of the art in each open problem.
引用
收藏
页码:46 / 58
页数:13
相关论文
共 66 条
[1]  
ANDO T, 1991, LECT NOTES
[2]  
[Anonymous], 2010, Recent Advances in Optimization and Its Applications in Engineering, DOI DOI 10.1007/978-3-642-12598-0_1
[3]   The maximal cp-rank of rank k completely positive matrices [J].
Barioli, F ;
Berman, A .
LINEAR ALGEBRA AND ITS APPLICATIONS, 2003, 363 :17-33
[4]   Chains of dog-ears for completely positive matrices [J].
Barioli, F .
LINEAR ALGEBRA AND ITS APPLICATIONS, 2001, 330 (1-3) :49-66
[5]   Completely positive matrices with a book-graph [J].
Barioli, F .
LINEAR ALGEBRA AND ITS APPLICATIONS, 1998, 277 (1-3) :11-31
[6]   COMBINATORIAL RESULTS ON COMPLETELY POSITIVE MATRICES [J].
BERMAN, A ;
HERSHKOWITZ, D .
LINEAR ALGEBRA AND ITS APPLICATIONS, 1987, 95 :111-125
[7]   BIPARTITE COMPLETELY POSITIVE MATRICES [J].
BERMAN, A ;
GRONE, R .
MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1988, 103 :269-276
[8]  
Berman A., 2003, Completely Positive Matrices
[9]  
Berman A., LINEAR ALGE IN PRESS
[10]  
Berman A., OPTIMIZATIO IN PRESS