TY - GEN
T1 - A Proof of the monotone column permanent (MCP) conjecture for dimension 4 via sums-of-squares of rational functions
AU - Kaltofen, Erich
AU - Yang, Zhengfeng
AU - Zhi, Lihong
PY - 2009
Y1 - 2009
N2 - semidefinite programming, sum-of-squares, Monotone Column Permanent Conjecture, hybrid method For a proof of the monotone column permanent (MCP) conjecture for dimension 4 it is sufficient to show that 4 polynomials, which come from the permanents of real matrices, are nonnegative for all real values of the variables, where the degrees and the number of the variables of these polynomials are all 8. Here we apply a hybrid symbolic-numerical algorithm for certifying that these polynomials can be written as an exact fraction of two polynomial sums -of-squares (SOS) with rational coefficients.
AB - semidefinite programming, sum-of-squares, Monotone Column Permanent Conjecture, hybrid method For a proof of the monotone column permanent (MCP) conjecture for dimension 4 it is sufficient to show that 4 polynomials, which come from the permanents of real matrices, are nonnegative for all real values of the variables, where the degrees and the number of the variables of these polynomials are all 8. Here we apply a hybrid symbolic-numerical algorithm for certifying that these polynomials can be written as an exact fraction of two polynomial sums -of-squares (SOS) with rational coefficients.
KW - Hybrid method
KW - Monotone Column Permanent Conjecture
KW - Semidefinite programming
KW - Sum-of-squares
UR - https://www.scopus.com/pages/publications/70450199445
U2 - 10.1145/1577190.1577204
DO - 10.1145/1577190.1577204
M3 - 会议稿件
AN - SCOPUS:70450199445
SN - 9781605586649
T3 - Proceedings of the 2009 Conference on Symbolic Numeric Computation, SNC 2009
SP - 65
EP - 69
BT - Proceedings of the 2009 Conference on Symbolic Numeric Computation, SNC 2009
T2 - 2009 Conference on Symbolic Numeric Computation, SNC 2009
Y2 - 3 August 2009 through 5 August 2009
ER -