Semidefinite programming for discrete optimization and matrix completion problems
Discrete Applied Mathematics
Ellipsoidal Approach to Box-Constrained Quadratic Problems
Journal of Global Optimization
Optimal pulse control of dynamic systems in the shock phase
Automation and Remote Control
On zero duality gap in nonconvex quadratic programming problems
Journal of Global Optimization
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A characterization is given for the spectrum of a symmetric matrix to remain real after a nonsymmetric sign-restricted border perturbation, including the case where the perturbation is skew-symmetric. The characterization is in terms of the stationary points of a quadratic function on the unit sphere. This yields interlacing relationships between the eigenvalues of the original matrix and those of the perturbed matrix. As a result of the linkage between the perturbation and stationarity problems, new theoretical insights are gained for each. Applications of the main results include a characterization of those matrices that are exponentially nonnegative with respect to the $n$-dimensional ice-cream cone, which in turn leads to a decomposition theorem for such matrices. In addition, results are obtained for nonsymmetric matrices regarding interlacing and majorization.