We establish in this paper optimal parametric Lagrangian dual models for box constrained quadratic program based on the generalized D.C.(difference between convex) optimization approach,which can be reformulated as se...We establish in this paper optimal parametric Lagrangian dual models for box constrained quadratic program based on the generalized D.C.(difference between convex) optimization approach,which can be reformulated as semidefinite programming problems.As an application,we propose new valid linear constraints for rank-one relaxation.展开更多
Motivated by the fact that not all nonconvex optimization problems are difficult to solve,we survey in this paper three widely used ways to reveal the hidden convex structure for different classes of nonconvex optimiz...Motivated by the fact that not all nonconvex optimization problems are difficult to solve,we survey in this paper three widely used ways to reveal the hidden convex structure for different classes of nonconvex optimization problems.Finally,ten open problems are raised.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos. 11001006 and 91130019/A011702)the Fund of State Key Laboratory of Software Development Environment (Grant No. SKLSDE-2011ZX-15.)
文摘We establish in this paper optimal parametric Lagrangian dual models for box constrained quadratic program based on the generalized D.C.(difference between convex) optimization approach,which can be reformulated as semidefinite programming problems.As an application,we propose new valid linear constraints for rank-one relaxation.
基金This research was supported by the National Natural Science Foundation of China(Nos.11822103,11571029)Natural Science Foundation of Beijing(No.Z180005).
文摘Motivated by the fact that not all nonconvex optimization problems are difficult to solve,we survey in this paper three widely used ways to reveal the hidden convex structure for different classes of nonconvex optimization problems.Finally,ten open problems are raised.
