A new optimal finite-time distributed linear averaging (OFTDLA) problem is presented in this paper. This problem is motivated from the distributed averaging problem which arises in the context of distributed algorithms in computer science and coordination of groups of autonomous agents in engineering. The aim of the OFTDLA problem is to compute the average of the initial values in finite-time s...

In this paper, we deal with the problem of constrained code optimization for radar Space-Time Adaptive Processing (STAP) in the presence of colored Gaussian disturbance. At the design stage, we devise a code design algorithm complying with the following optimality criterion: maximization of the detection performance under a control on the regions of achievable values for the temporal and spatia...

In this lecture, we will discuss one of the most important applications of semidefinite programming, namely its use in the formulation of convex relaxations of nonconvex optimization problems. We will present the results from several different, but complementary, points of view. These will also serve us as starting points for the generalizations to be presented later in the course. We will disc...

In this lecture, we will discuss one of the most important applications of semidefinite programming, namely its use in the formulation of convex relaxations of nonconvex optimization problems. We will present the results from several different, but complementary, points of view. These will also serve us as starting points for the generalizations to be presented later in the course. We will disc...

In this paper we consider the problem of computing the value and a supporting hyperplane of the convex envelope for quadratic and polynomial functions over polytopes with known vertex set. We show that for general quadratic functions the computation can be carried on through a copositive problem, but in some cases (including all the two-dimensional ones) we can solve a semidefinite problem. The...

In this paper, we discuss semidefinite relaxation techniques for computing minimal size ellipsoids that bound the solution set of a system of uncertain linear equations (ULE). The proposed technique is based on the combination of a quadratic embedding of the uncertainty, and the Sprocedure. The resulting bounding condition is expressed as a Linear Matrix Inequality (LMI) constraint on the ellip...

In this paper, we consider minimizing the ratio of two indefinite quadratic functions subject to two quadratic constraints. Using the extension of Charnes– Cooper transformation, we transform the problem to a homogenized quadratic problem. Then, we show that, under certain assumptions, it can be solved to global optimality using semidefinite optimization relaxation.

A robust structural optimization scheme as well as an optimization algorithm are presented based on the robustness function. Under the uncertainties of external forces based on the info-gap model, the maximization problem of the robustness function is formulated as an optimization problem with infinitely many constraints. By using the quadratic embedding technique of uncertainty and the S-proce...

We consider the problem of estimating a vector z in the regression model b = Az+w, where w is an unknown but bounded noise. As in many regularization schemes, we assume that an upper bound on the norm of z is available. To estimate z we propose a relaxation of the Chebyshev center, which is the vector that minimizes the worst-case estimation error over all feasible vectors z. Relying on recent ...

Abstract. We consider a conic-quadratic (and in particular a quadratically constrained) optimization problem with uncertain data, known only to reside in some uncertainty set U . The robust counterpart of such a problem leads usually to an NP-hard semidefinite problem; this is the case, for example, when U is given as the intersection of ellipsoids or as an n-dimensional box. For these cases we...