SIAM Review
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
On Standard Quadratic Optimization Problems
Journal of Global Optimization
Introduction to Global Optimization (Nonconvex Optimization and Its Applications)
Introduction to Global Optimization (Nonconvex Optimization and Its Applications)
On Copositive Programming and Standard Quadratic Optimization Problems
Journal of Global Optimization
Dual Bounds and Optimality Cuts for All-Quadratic Programs with Convex Constraints
Journal of Global Optimization
Branch-and-bound approaches to standard quadratic optimization problems
Journal of Global Optimization
Computational Optimization and Applications
A clique algorithm for standard quadratic programming
Discrete Applied Mathematics
Multiterm polyhedral relaxations for nonconvex, quadratically constrained quadratic programs
Optimization Methods & Software - GLOBAL OPTIMIZATION
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The paper describes a method for computing a lower bound of the global minimum of an indefinite quadratic form over a simplex. The bound is derived by computing an underestimator of the convex envelope by solving a semidefinite program (SDP). This results in a convex quadratic program (QP). It is shown that the optimal value of the QP is a lower bound of the optimal value of the original problem. Since there exist fast (polynomial time) algorithms for solving SDP‘s and QP‘s the bound can be computed in reasonable time. Numerical experiments indicate that the relative error of the bound is about 10 percent for problems up to 20 variables, which is much better than a known SDP bound.