TY - JOUR
T1 - Quadratic maximization and semidefinite relaxation
AU - Zhang, Shuzhong
PY - 2000/5
Y1 - 2000/5
N2 - In this paper we study a class of quadratic maximization problems and their semidefinite programming (SDP) relaxation. For a special subclass of the problems we show that the SDP relaxation provides an exact optimal solution. Another subclass, which is script Nscript P-hard, guarantees that the SDP relaxation yields an approximate solution with a worst-case performance ratio of 0.87856.... This is a generalization of the well-known result of Goemans and Williamson for the maximum-cut problem. Finally, we discuss extensions of these results in the presence of a certain type of sign restrictions.
AB - In this paper we study a class of quadratic maximization problems and their semidefinite programming (SDP) relaxation. For a special subclass of the problems we show that the SDP relaxation provides an exact optimal solution. Another subclass, which is script Nscript P-hard, guarantees that the SDP relaxation yields an approximate solution with a worst-case performance ratio of 0.87856.... This is a generalization of the well-known result of Goemans and Williamson for the maximum-cut problem. Finally, we discuss extensions of these results in the presence of a certain type of sign restrictions.
KW - Approximation
KW - Polynomial-time algorithm
KW - Quadratic programming
KW - Semidefinite programming relaxation
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U2 - 10.1007/s101070050006
DO - 10.1007/s101070050006
M3 - Article
AN - SCOPUS:0038029207
SN - 0025-5610
VL - 87
SP - 453
EP - 465
JO - Mathematical Programming, Series B
JF - Mathematical Programming, Series B
IS - 3
ER -