A new algorithm for solving the general quadratic programming problem
Computational Optimization and Applications
Duality bound method for the general quadratic programming problem with quadratic constraints
Journal of Optimization Theory and Applications
Dual Applications of Proximal Bundle Methods, Including Lagrangian Relaxation of Nonconvex Problems
SIAM Journal on Optimization
Solving a Class of Linearly Constrained Indefinite QuadraticProblems by D.C. Algorithms
Journal of Global Optimization
A Simplicial Branch-and-Bound Method for Solving Nonconvex All-Quadratic Programs
Journal of Global Optimization
A New Semidefinite Programming Bound for Indefinite Quadratic Forms Over a Simplex
Journal of Global Optimization
Introduction to Global Optimization (Nonconvex Optimization and Its Applications)
Introduction to Global Optimization (Nonconvex Optimization and Its Applications)
A class of problems where dual bounds beat underestimation bounds
Journal of Global Optimization
A bilinear formulation for vector sparsity optimization
Signal Processing
Box-constrained quadratic programs with fixed charge variables
Journal of Global Optimization
Multiterm polyhedral relaxations for nonconvex, quadratically constrained quadratic programs
Optimization Methods & Software - GLOBAL OPTIMIZATION
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A central problem of branch-and-bound methods for global optimization is that often a lower bound do not match with the optimal value of the corresponding subproblem even if the diameter of the partition set shrinks to zero. This can lead to a large number of subdivisions preventing the method from terminating in reasonable time. For the all-quadratic optimization problem with convex constraints we present optimality cuts which cut off a given local minimizer from the feasible set. We propose a branch-and-bound algorithm using optimality cuts which is finite if all global minimizers fulfill a certain second order optimality condition. The optimality cuts are based on the formulation of a dual problem where additional redundant constraints are added. This technique is also used for constructing tight lower bounds. Moreover we present for the box-constrained and the standard quadratic programming problem dual bounds which have under certain conditions a zero duality gap.