Let α = (α1, α2, · · · , αm) ∈ R>0. Let αi,j be the vector obtained from α by deleting the entries αi and αj . Besser and Moree [1] introduced some invariants and near invariants related to the solutions ∈ {±1}m−2 of the linear inequality |αi −αj | < 〈 , αi,j〉 < αi +αj , where 〈, 〉 denotes the usual inner product and αi,j the vector obtained from α by deleting αi and αj . The main result of Bes...

In this paper we consider correcting infeasibility in a second order conic linear inequality by minimal changes in the problem data. Under certain conditions, it is proved that the minimal correction can be done by solving a lower dimensional convex problem. Finally, several examples are presented to show the efficiency of the new approach.

In this paper, we propose a design method of a static anti-windup compensator that guarantees closed-loop stability and optimizes performance criterion proposed by Teel and Kapoor. Further, we extend the method to the robust performance problem. We provide design procedures based on linear matrix inequality (LMI) representation.

Based on linear matrix inequality (LMI) technique. a sliding mode control approach is presented for a class of uncertain time-delay systems in the delayindependent and delay-dependent case. The corresponding sufficient conditions for the existence of sliding mode are proposed. Different from the reported results. the conclusion presented in this paper is only relating to the original system par...

Assessing stability of time-delay systems based on the Lyapunov-Krasovskii functionals has been the subject of many contributions. Most of the results are based, first, on the design of more and more involved class of functionals and, finally, on the use of the famous Jensen’s inequality. In contrast with this design process, the present paper aims at providing a generic set of integral inequal...

Redundant constraints in linear inequality systems can be characterized as those inequalities that can be removed from an arbitrary linear optimization problem posed on its solution set without modifying its value and its optimal set. A constraint is saturated in a given linear optimization problem when it is binding at the optimal set. Saturation is a property related with the preservation of ...

The celebrated Farkas lemma originated in Farkas (1902) provides us an attractively simple and extremely useful characterization for a linear inequality to be a consequence of a linear inequality system on the Euclidean space Rn . This lemma has been extensively studied and extended in many directions, including conic systems (linear, sublinear, convex), infinite/semi-infinite convex inequality...

In this paper, we introduce the notion of sesquilinear map on Β(H) . Based on this notion, we define the quadratic map, which is the generalization of positive linear map. With the help of this concept, we prove several well-known equality and inequality...  

We develop in this paper an improvement of the method given by S. Bobkov and M. Ledoux in [BL00]. Using the Prékopa-Leindler inequality, we prove a modified logarithmic Sobolev inequality adapted for all measures on Rn, with a strictly convex and super-linear potential. This inequality implies modified logarithmic Sobolev inequality, developed in [GGM05, GGM07], for all uniformly strictly conve...

The normal linear model, with sign or other linear inequality constraints on its coefficients, arises very commonly in many scientific applications. Given inequality constraints Bayesian inference is much simpler than classical inference, but standard Bayesian computational methods become impractical when the posterior probability of the inequality constraints (under a diffuse prior) is small. ...