The aim of this paper is to show a simple way to construct asymptotic minimax lower bounds for risks based on different types of quadratic loss functions in semiparametric inference problems. For the sake of clarity, we consider the simple case of the state estimation of a dynamical system with small noise. The proofs are based on the van Trees inequality, namely an integral type Cramér-Rao ine...

In this paper we obtain some simple characterizations of the solution sets of a pseudoconvex program and a variational inequality. Similar characterizations of the solution set of a quasiconvex quadratic program are derived. Applications of these characterizations are given.

We use the method of positive quadratic forms and discrete analogues of the Laguerre inequality recently obtained by the author, to give bounds on the zeros of the Charlier polynomials, which are uniform in all parameters involved.

In this paper we obtain some inequalities related to the generalized triangle and quadratic triangle inequalities for vectors in inner product spaces. Some results that employ the Ostrowski discrete inequality for vectors in normed linear spaces are also obtained.

This paper deals with the stabilization of TakagiSugeno fuzzy models. Using non-quadratic Lyapunov function, new sufficient stabilization criteria with PDC controller are established in terms of Linear Matrix Inequality. Finally, a stabilization condition for uncertain system is given.

We consider a chance constraint Prob{ξ : A(x, ξ) ∈ K} ≥ 1 − 2 (x is the decision vector, ξ is a random perturbation, K is a closed convex cone, and A(·, ·) is bilinear). While important for many applications in Optimization and Control, chance constraints typically are “computationally intractable”, which makes it necessary to look for their tractable approximations. We present these approximat...

This article proves an exponential probability tail inequality for positive semidefinite quadratic forms in a subgaussian random vector. The bound is analogous to one that holds when the vector has independent Gaussian entries.

We prove an inequality involving the degeneracy, the cutwidth and the sparsity of graphs. It implies a quadratic lower bound on the cutwidth in terms of the degeneracy for all graphs and an improvement of it for clique-free graphs.

The relationship between the mathematical program with linear complementarity constraints (MPCC) and its inequality relaxation is studied. A new sequential quadratic programming (SQP) method is presented for solving the MPCC based on this relationship. A certain SQP technique is introduced to deal with the possible infeasibility of quadratic programming subproblems. Global convergence results a...

Abstract. We are interested in the Logarithmic Sobolev Inequality for the infinite volume Gibbs measure with no quadratic interactions. We consider unbounded spin systems on the one dimensional Lattice with interactions that go beyond the usual strict convexity and without uniform bound on the second derivative. We assume that the one dimensional single-site measure with boundaries satisfies th...