In this paper, the simultaneous stabilization problem is considered using the matrix inequality approach. Some necessary and sufficient conditions for simultaneous stabilizability of r strictly proper multi-input/multi-output (MIMO) plants via static output feedback and state feedback are obtained in the form of coupled ARI’s. It is shown that any such stabilizing feedback gain is the solution ...

This paper presents and studies the iteration-complexity of two new inexact variants of Rockafellar’s proximal method of multipliers (PMM) for solving convex programming (CP) problems with a finite number of functional inequality constraints. In contrast to the first variant which solves convex quadratic programming (QP) subproblems at every iteration, the second one solves convex constrained q...

This paper deals with the problem of absolute stability of neutral type Lur’e systems with time-varying delays. By constructing new Lyapunov-Krasovskii functional, a matrix-based on quadratic convex approach combining with some improved bounding techniques for integral terms such as Wirtinger-based integral inequality, new stability condition is much less conservative and more general than some...

Abstract. We show that the quadratic transportation cost inequality T2 is equivalent to both a Poincaré inequality and a strong form of the Gaussian concentration property. The main ingredient in the proof is a new family of inequalities, called modified quadratic transportation cost inequalities in the spirit of the modified logarithmic-Sobolev inequalities by Bobkov and Ledoux [6], that are s...

Moment inequality for quadratic forms of random vectors is of particular interest in covariance matrix testing and estimation problems. In this paper, we prove a Rosenthal-type inequality, which exhibits new features and certain improvement beyond the unstructured Rosenthal inequality of quadratic forms when dimension of the vectors increases without bound. Applications to test the block diagon...

We present a new method for solving the box-constrained stochastic linear variational inequality problem with three special types of uncertainty sets. Most previous methods, such as the expected value and expected residual minimization, need the probability distribution information of the stochastic variables. In contrast, we give the robust reformulation and reformulate the problem as a quadra...

let x ,..., xn 1 be a random sample from a distribution with sample mean x and samplevariance s 2. in this paper we consider certain very general properties of the so-called “z-scores”x x s i n i ( − )/ : = 1,...., . a representation theorem is then given for z-scores obtained from an underlyingnormal population, together with a theorem for their limiting distribution as the sample size tends t...

‎in this paper‎, ‎some kkt type sufficient global optimality conditions‎ ‎for general mixed integer nonlinear programming problems with‎ ‎equality and inequality constraints (minpp) are established‎. ‎we achieve‎ ‎this by employing a lagrange function for minpp‎. ‎in addition‎, ‎verifiable sufficient global optimality conditions for general mixed‎ ‎integer quadratic programming problems are der...

In this paper we extend the notion of g-evaluation, in particular g-expectation, of Peng [10, 11] to the case where the generator g is allowed to have a quadratic growth. We show that some important properties of the g-expectations, including a representation theorem between the generator and the corresponding g-expectation, and consequently the reverse comparison theorem of quadratic BSDEs as ...

The problem of giving a spectral factorization of a class of matrices arising in Wiener filtering theory and network synthesis is tackled via an kgebralc procedure. A quadratic matrix quation involving only constant matrices is shown to possess solutions which directly define a solution to the spectral factorization problem. A spectral factor with a stable inverse is defined by that unique solu...