Kazhdan’s Property (T) via Semidefinite Optimization

On solving biquadratic optimization via semidefinite relaxation

In this paper, we study a class of biquadratic optimization problems. We first relax the original problem to its semidefinite programming (SDP) problem and discuss the approximation ratio between them. Under some conditions, we show that the relaxed problem is tight. Then we consider how to approximately solve the problems in polynomial time. Under several different constraints, we present vari...

Bounds on linear PDEs via semidefinite optimization

Using recent progress on moment problems, and their connections with semidefinite optimization, we present in this paper a new methodology based on semidefinite optimization, to obtain a hierarchy of upper and lower bounds on linear functionals defined on solutions of linear partial differential equations. We apply the proposed method to examples of PDEs in one and two dimensions, with very enc...

Semidefinite Optimization

Semidefinite Optimization ∗

Optimization problems in which the variable is not a vector but a symmetric matrix which is required to be positive semidefinite have been intensely studied in the last ten years. Part of the reason for the interest stems from the applicability of such problems to such diverse areas as designing the strongest column, checking the stability of a differential inclusion, and obtaining tight bounds...

On Approximating Complex Quadratic Optimization Problems via Semidefinite Programming Relaxations

In this paperwe study semidefinite programming (SDP)models for a class of discrete and continuous quadratic optimization problems in the complex Hermitian form. These problems capture a class of well-known combinatorial optimization problems, as well as problems in control theory. For instance, they include theMAX-3-CUT problem where the Laplacian matrix is positive semidefinite (in particular,...