A new algorithm for solving the general quadratic programming problem
Computational Optimization and Applications
The symmetric eigenvalue problem
The symmetric eigenvalue problem
Journal of Optimization Theory and Applications
A mathematical view of interior-point methods in convex optimization
A mathematical view of interior-point methods in convex optimization
Solving a Class of Linearly Constrained Indefinite QuadraticProblems by D.C. Algorithms
Journal of Global Optimization
On Standard Quadratic Optimization Problems
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
On solving the maximum clique problem
Journal of Global Optimization
Branch-and-bound approaches to standard quadratic optimization problems
Journal of Global Optimization
Target-Oriented Branch and Bound Method for Global Optimization
Journal of Global Optimization
Journal of Global Optimization
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In this paper we analyze difference-of-convex (d.c.) decompositions for indefinite quadratic functions. Given a quadratic function, there are many possible ways to decompose it as a difference of two convex quadratic functions. Some decompositions are dominated, in the sense that other decompositions exist with a lower curvature. Obviously, undominated decompositions are of particular interest. We provide three different characterizations of such decompositions, and show that there is an infinity of undominated decompositions for indefinite quadratic functions. Moreover, two different procedures will be suggested to find an undominated decomposition starting from a generic one. Finally, we address applications where undominated d.c.d.s may be helpful: in particular, we show how to improve bounds in branch-and-bound procedures for quadratic optimization problems.