We study constrained and unconstrained optimization programs for nonconvex maximum eigenvalue functions. We show how second order techniques may be introduced as soon as it is possible to reliably guess the multiplicity of the maximum eigenvalue at a limit point. We examine in which way standard and projected Newton steps may be combined with a nonsmooth first-order method to obtain a globally ...

High-dimensional eigenproblems often arise in the solution of scientiic problems involving stability or wave modeling. In this article we present results for a quadratic eigenproblem that we encountered in solving an acoustics problem, speciically in modeling the propagation of waves in a room in which one wall was constructed of sound-absorbing material. EEcient algorithms are known for the st...

Let S ⊂ R3 be a C4-smooth relatively compact orientable surface with a sufficiently regular boundary. For β ∈ R+, let Ej(β) denote the jth negative eigenvalue of the operator associated with the quadratic form H(R) ∋ u 7→ ∫∫∫

Clifford A. Meyer and Christodoulos A. Floudas Department of Chemical Engineering, Princeton University, Princeton, NJ 08544, USA Abstract This paper presents an efficient branch and bound approach to address the global optimization of constrained optimization problems with twice differentiable functions. A lower bound on the global minimum is determined via a convex nonlinear programming probl...

A quantitative version of the Oppenheim conjecture for inhomogeneous quadratic forms is proved. We also give an application to eigenvalue spacing on flat 2-tori with Aharonov-Bohm flux.

The purpose of this paper is to show how the problem of finding the zeros of unilateral n-order quaternionic polynomials can be solved by determining the eigenvectors of the corresponding companion matrix. This approach, probably superfluous in the case of quadratic equations for which a closed formula can be given, becomes truly useful for (unilateral) n-order polynomials. To understand the st...