### A branch-and-cut algorithm for nonconvex quadratic programs with box constraints

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**Papers and Publications**

Gao , Solutions and optimality criteria to box constrained nonconvex minimization problems, Journal of Industrial and Management Optimization , 3 , Li , Trust-region problems with linear inequality constraints: Exact SDP relaxation, global optimality and robust optimization, Mathematical Programming , , Kojima , Second order cone programming relaxation of nonconvex quadratic optimization problems, Optimization Methods and Software , 15 , Jin , An eigenvalue decomposition based branch-and-bound algorithm for nonconvex quadratic programming problems with convex quadratic constraints, Journal of Global Optimization , 67 , Vavasis , Quadratic programming with one negative eigenvalue is NP-hard, Journal of Global Optimization , 1 , Sturm , Using SeDuMi 1.

Zhang , On cones of nonnegative quadratic functions, Mathematics of Operations Research , 28 , Feng , Congruence diagonalization of two Hermite matrices simultaneously, International Journal of Algebra , 4 , Xing , Detection of a copositive matrix over a p-th order cone, Pacific Journal of Optimization , 10 , Xing , Conic approximation to quadratic optimization with linear complementarity constraints, Computational Optimization and Applications , 66 , Zhou and Z.

Xu, A simultaneous diagonalization based SOCP relaxation for convex quadratic programs with linear complementarity constraints, Optimization Letters , Download as excel. Ziye Shi , Qingwei Jin. Second order optimality conditions and reformulations for nonconvex quadratically constrained quadratic programming problems. Yanqin Bai , Chuanhao Guo. Doubly nonnegative relaxation method for solving multiple objective quadratic programming problems.

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Second order sufficient conditions for a class of bilevel programs with lower level second-order cone programming problem. Anwa Zhou , Jinyan Fan. A semidefinite relaxation algorithm for checking completely positive separable matrices. Ye Tian , Cheng Lu. Nonconvex quadratic reformulations and solvable conditions for mixed integer quadratic programming problems. Immediate schedule adjustment and semidefinite relaxation. Duality formulations in semidefinite programming. Convergence analysis of a nonlinear Lagrangian method for nonconvex semidefinite programming with subproblem inexactly solved.

Yang Li , Liwei Zhang. A nonlinear Lagrangian method based on Log-Sigmoid function for nonconvex semidefinite programming. Xinmin Yang. On second order symmetric duality in nondifferentiable multiobjective programming.

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