TY - JOUR
T1 - A Polynomial Optimization Framework for Polynomial Quasi-variational Inequalities with Moment-sos Relaxations
AU - Tang, Xindong
AU - Zhang, Min
AU - Zhong, Wenzhi
N1 - Xindong Tang is supported by the NSFC Young Scientists Fund, grant number [12301407]. Min Zhang is supported by the National Natural Science Foundation of China Youth Fund Project, grant number [12101598].
PY - 2024/12
Y1 - 2024/12
N2 - We consider quasi-variational inequality problems (QVI) given by polynomial functions. By applying Lagrange multiplier expressions, we formulate polynomial optimization problems whose minimizers are KKT points for the QVI. Then, feasible extensions are exploited to preclude KKT points that are not solutions. Moment-SOS relaxations are incorporated to solve the polynomial optimization problems in our methods. Under certain conditions, our approach guarantees to find a solution to the QVI or detect the nonexistence of solutions.
AB - We consider quasi-variational inequality problems (QVI) given by polynomial functions. By applying Lagrange multiplier expressions, we formulate polynomial optimization problems whose minimizers are KKT points for the QVI. Then, feasible extensions are exploited to preclude KKT points that are not solutions. Moment-SOS relaxations are incorporated to solve the polynomial optimization problems in our methods. Under certain conditions, our approach guarantees to find a solution to the QVI or detect the nonexistence of solutions.
KW - Lagrange multiplier expression
KW - Moment-SOS hierarchy
KW - Quasi-variational inequality
KW - Polynomial optimization
UR - https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=hkbuirimsintegration2023&SrcAuth=WosAPI&KeyUT=WOS:001373242700001&DestLinkType=FullRecord&DestApp=WOS_CPL
U2 - 10.3934/naco.2024054
DO - 10.3934/naco.2024054
M3 - Journal article
SN - 2155-3289
JO - Numerical Algebra, Control and Optimization
JF - Numerical Algebra, Control and Optimization
ER -