TY - JOUR
T1 - Extension of Completely Positive Cone Relaxation to Moment Cone Relaxation for Polynomial Optimization
AU - Arima, Naohiko
AU - Kim, Sunyoung
AU - Kojima, Masakazu
N1 - Funding Information:
The research of Sunyoung Kim was supported by NRF 2012-R1A1A2-038982 and NRF 2014-R1A2A1A11049618.
Publisher Copyright:
© 2015, Springer Science+Business Media New York.
PY - 2016/3/1
Y1 - 2016/3/1
N2 - We propose the moment cone relaxation for a class of polynomial optimization problems to extend the results on the completely positive cone programming relaxation for the quadratic optimization model by Arima, Kim and Kojima. The moment cone relaxation is constructed to take advantage of sparsity of the polynomial optimization problems, so that efficient numerical methods can be developed in the future. We establish the equivalence between the optimal value of the polynomial optimization problem and that of the moment cone relaxation under conditions similar to the ones assumed in the quadratic optimization model.
AB - We propose the moment cone relaxation for a class of polynomial optimization problems to extend the results on the completely positive cone programming relaxation for the quadratic optimization model by Arima, Kim and Kojima. The moment cone relaxation is constructed to take advantage of sparsity of the polynomial optimization problems, so that efficient numerical methods can be developed in the future. We establish the equivalence between the optimal value of the polynomial optimization problem and that of the moment cone relaxation under conditions similar to the ones assumed in the quadratic optimization model.
KW - Completely positive programming
KW - Copositive programming
KW - Moment cone relaxation
KW - Polynomial optimization
UR - http://www.scopus.com/inward/record.url?scp=84959167628&partnerID=8YFLogxK
U2 - 10.1007/s10957-015-0794-9
DO - 10.1007/s10957-015-0794-9
M3 - Article
AN - SCOPUS:84959167628
VL - 168
SP - 884
EP - 900
JO - Journal of Optimization Theory and Applications
JF - Journal of Optimization Theory and Applications
SN - 0022-3239
IS - 3
ER -