Error Bounds for Eigenvalue and Semidefinite Matrix Inequality Systems
نویسندگان
چکیده
In this paper we give sufficient conditions for existence of error bounds for systems expressed in terms of eigenvalue functions (such as in eigenvalue optimization) or positive semidefiniteness (such as in semidefinite programming).
منابع مشابه
MATHEMATICAL ENGINEERING TECHNICAL REPORTS Eigenvalue Optimization of Structures via Polynomial Semidefinite Programming
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 ...
متن کاملKnapsack-Based Cutting Planes for the Max-Cut Problem
We present a new procedure for generating cutting planes for the max-cut problem. The procedure consists of three steps. First, we generate a violated (or near-violated) linear inequality that is valid for the semidefinite programming (SDP) relaxation of the max-cut problem. This can be done by computing the minimum eigenvalue of a certain matrix. Second, we use this linear inequality to constr...
متن کاملExponential error rates of SDP for block models: Beyond Grothendieck's inequality
In this paper we consider the cluster estimation problem under the Stochastic Block Model. We show that the semidefinite programming (SDP) formulation for this problem achieves an error rate that decays exponentially in the signal-to-noise ratio. The error bound implies weak recovery in the sparse graph regime with bounded expected degrees, as well as exact recovery in the dense regime. An imme...
متن کاملAn Eigenvalue Majorization Inequality for Positive Semidefinite Block Matrices: In Memory of Ky Fan
2 Let H = [ M K K∗ N ] be a Hermitian matrix. It is known that the eigenvalues of M ⊕N are 3 majorized by the eigenvalues of H . If, in addition, H is positive semidefinite and the block K 4 is Hermitian, then the following reverse majorization inequality holds for the eigenvalues: 5
متن کاملGlobal optimization for the Biaffine Matrix Inequality problem
It has recently been shown that an extremely wide array of robust controller design problems may be reduced to the problem of finding a feasible point under a Biaffine Matrix Inequality (BMI) constraint. The BMI feasibility problem is the bilinear version of the Linear (Affine) Matrix Inequality (LMI) feasibility problem, and may also be viewed as a bilinear extension to the Semidefinite Progra...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Math. Program.
دوره 104 شماره
صفحات -
تاریخ انتشار 2005