A Global Algorithm for Quadratic Programming with One Negative Eigenvalue Based on Successive Linear Conic Optimization and Convex Relaxation
نویسندگان
چکیده
We consider quadratic programs with a single negative eigenvalue (QP1NE) subject to linear and conic constraints. The QP1NE model covers the classical clique problem that is known to be NP-hard [26]. In this paper, by combining successive linear conic optimization (SLCO), convex relaxation and line search technique, we present a global algorithm for QP1NE which can locate a global optimal solution to the underlying QP1NE within ǫ-tolerance via solving at most O( tu−tl √ ǫ log tu−tl √ ǫ ) linear conic optimization problems, where tu and tl are the upper and lower bounds of t, respectively, and −t is the only negative quadratic term in the objective function. Promising numerical results are reported.
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