The Smoothing Method For The Polyhedral Cone Constrained Eigenvalue Problem

The polyhedral cone constrained eigenvalue problem is considered in thispaper, which contains the following contents:In chapter1, we give an introduction of the polyhedral cone constrainedeigenvalue problem, which mainly discusses the current development of the dis-cussed issue. We reformulate the polyhedral cone constrained eigenvalue problemas a unconstrained optimization problem.In chapter2, for the polyhedral cone constrained eigenvalue problem, basedon its nonsmooth transformed version and a smoothing technique, we proposea smoothing Broyden-like method which makes use of the derivative-free linesearch. Global and local superlinear convergence results of this method are es-tablished under suitable conditions. The given computational experiments showthe efciency of this method.In chapter3, for the polyhedral cone constrained eigenvalue problem, basedon its nonsmooth transformed version and a smoothing technique, we propose amodified Newton method which makes use of the searching direction computedby the Newton equation or the gradient of function depending on the consistenceof the Newton equation and the sufcient descent of the Newton direction. Weestablish its convergence under suitable conditions. Some numerical examples aregiven to illustrate the performance and efciency of this method.