The problem of nding the smallest eigenvalue and the corresponding eigenspace of a symmetric matrix is stated as a semide nite optimization problem. A straightforward application of nowadays more or less standard routines for the solution of semide nite problems yields a new algorithm for the smallest eigenvalue problem; the approach not only yields the smallest eigenvalue, but also a symmetric...

An inverse eigenvalue problem approach to system design is considered. The Cayley-Hamilton theorem is developed for the general case involving the generalized eigenvalue vibration problem. Since many solutions exist for a desired frequency spectrum, a discussion of the required design information and suggestions for including structural constraints are given. An algorithm for solving the invers...

We study the extension of a column generation technique to eigenvalue optimization. In our approach we utilize the method of analytic center to obtain the query points at each iteration. A restricted master problem in the primal space is formed corresponding to the relaxed dual problem. At each step of the algorithm, an oracle is called to return the necessary columns to update the restricted m...

Optimization of convex functions subject to eigenvalue constraints is intriguing because of peculiar analytical properties of eigenvalue functions and is of practical interest because of a wide range of applications in fields such as structural design and control theory. Here we focus on the optimization of a linear objective subject to a constraint on the smallest eigenvalue of an analytic and...

This paper addresses the impact of the structure of the viral propagation network on the viral prevalence. For that purpose, a new epidemic model of computer virus, known as the node-based SLBS model, is proposed. Our analysis shows that the maximum eigenvalue of the underlying network is a key factor determining the viral prevalence. Specifically, the value range of the maximum eigenvalue is p...

This paper discusses finite-element highly efficient calculation schemes for solving eigenvalue problem of electric field. Multigrid discretization is extended to the filter approach for eigenvalue problem of electric field. With this scheme one solves an eigenvalue problem on a coarse grid just at the first step, and then always solves a linear algebraic system on finer and finer grids. Theore...

‎based on an eigenvalue analysis‎, ‎a new proof for the sufficient‎ ‎descent property of the modified polak-ribière-polyak conjugate‎ ‎gradient method proposed by yu et al‎. ‎is presented‎.

In the present research, the elastic buckling of composite cross-ply elliptical cylindrical shells under axial compression is studied through finite element approach. The formulation is based on shear deformation theory and the serendipity quadrilateral eight-node element is used to study the elastic behavior of elliptical cylindrical shells. The strain-displacement relations are accurately acc...

This paper presents a sequential semidefinite programming (SDP) approach to maximize the minimal eigenvalue of the generalized eigenvalue problem, in which the two symmetric matrices defining the eigenvalue problem are supposed to be the polynomials in terms of the variables. An important application of this problem is found in the structural optimization which attempts to maximize the minimal ...

It was conjectured by Doron and Smilansky (DS) in 1992 that k2 > 0 is a Dirichlet eigenvalue of the Laplacian in a bounded domain D if and only if the corresponding S-matrix for the scattering problem by the obstacle D has an eigenvalue 1. The main results of this paper are: 1) a proof that the DS conjecture is incorrect, 2) a proof that a necessary condition for 1 to be an eigenvalue of the S-...