scholarly journals Strongly regular points of mappings

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Malek Abbasi ◽  
Michel Théra
Keyword(s):  
Error Bound ◽  
Directional Derivative ◽  
Sufficient Conditions ◽  
Strong Regularity ◽  
Strongly Regular

AbstractIn this paper, we use a robust lower directional derivative and provide some sufficient conditions to ensure the strong regularity of a given mapping at a certain point. Then, we discuss the Hoffman estimation and achieve some results for the estimate of the distance to the set of solutions to a system of linear equalities. The advantage of our estimate is that it allows one to calculate the coefficient of the error bound.

scholarly journals Exact Penalization in Stochastic Programming—Calmness and Constraint Qualification

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Martin Branda
Keyword(s):  
Stochastic Programming ◽  
Error Bound ◽  
Constraint Qualification ◽  
Sufficient Conditions ◽  
Discrete Distributions ◽  
Exact Penalty ◽  
Asymptotic Equivalence ◽  
Exact Penalization ◽  
Local Minimizers ◽  
Constrained Problems

We deal with the conditions which ensure exact penalization in stochastic programming problems under finite discrete distributions. We give several sufficient conditions for problem calmness including graph calmness, existence of an error bound, and generalized Mangasarian-Fromowitz constraint qualification. We propose a new version of the theorem on asymptotic equivalence of local minimizers of chance constrained problems and problems with exact penalty objective. We apply the theory to a problem with a stochastic vanishing constraint.

scholarly journals Strong Regularity in Arbitrary Rings

1952 ◽  
Vol 4 ◽  
pp. 51-53 ◽  
Author(s):  
Tetsuo Kandô
Keyword(s):  
Matrix Ring ◽  
Strong Regularity ◽  
Full Matrix ◽  
Regular Ideal ◽  
Strongly Regular ◽  
Full Matrix Ring

An element a of a ring R is called regular, if there exists an element x of R such that a×a = a, and a two-sided ideal a in R is said to be regular if each of its elements is regular B. Brown and N. H. McCoy [1] has recently proved that every ring R has a unique maximal regular two-sided ideal M(R), and that M(R) has the following radical-like property: (i) M(R/M(R)) = 0; (ii) if a is a two-sided ideal of R, then M(a) = a ∩ M(R); (iii) M(Rn) = (M(R))n, where Rn denotes a full matrix ring of order n over R. Arens and Kaplansky [2] has defined an element a of R to be strongly regular when there exists an element x of R such that a2x = a. We shall prove in this note that replacing “regularity” by “strong regularity,” we have also a unique maximal strongly regular ideal N(R), and shall investigate some of its properties.

TABLE ALGEBRAS OF RANK 3 AND ITS APPLICATIONS TO STRONGLY REGULAR GRAPHS

2013 ◽  
Vol 12 (05) ◽  
pp. 1250216 ◽  
Author(s):  
A. HOSSEINI ◽  
A. RAHNAMAI BARGHI
Keyword(s):  
Regular Graph ◽  
Coding Theory ◽  
Sufficient Conditions ◽  
Algebraic Approach ◽  
Strongly Regular Graph ◽  
Direct Consequence ◽  
Primitive Idempotents ◽  
Strongly Regular ◽  
Table Algebra ◽  
Integral Table Algebra

A table algebra is called quasi self-dual if there exists a permutation on the set of primitive idempotents under which any Krein parameter is equal to its corresponding structure constants. In this paper we investigate the question of when a table algebra of rank 3 is quasi self-dual. As a direct consequence we find necessary and sufficient conditions for the Bose–Mesner algebra of a given strongly regular graph to be quasi self-dual. In fact, our result generalizes the well-known Delsarte's characterization of a self-duality of the Bose–Mesner algebra of a strongly regular graph given in [P. Delsarte, An algebraic approach to the association schemes of coding theory, Philips Res. Rep. Suppl.10 (1973) 1–97]. Among our results we determine conditions under which the Krein parameters of an integral table algebra of rank 3 are non-negative rational numbers.

ROBUST SYNCHRONIZATION OF CHAOTIC LUR'E SYSTEMS VIA REPLACING VARIABLES CONTROL

2006 ◽  
Vol 16 (11) ◽  
pp. 3421-3433 ◽  
Author(s):  
XIAOFENG WU ◽  
MUHONG WANG
Keyword(s):  
Frequency Domain ◽  
Error Bound ◽  
Sufficient Conditions ◽  
Synchronization Error ◽  
Linear Matrix ◽  
Lur’E Systems ◽  
Parameter Mismatch ◽  
Chaotic Lur’E Systems ◽  
Definition Of ◽  
Synchronization Scheme

The sufficient conditions for chaos synchronization of two nonidentical systems by replacing variables control have not been proposed until now. In this paper, synchronization of two chaotic Lur'e systems with parameter mismatch by replacing variables control is studied. First of all, we present a master-slave Lur'e systems synchronization scheme with both parameter mismatch and replacing variables control, and derive a responsive error system for the scheme. A new definition of synchronization with finite L 2-gain is then introduced. Based on the definition, the sufficient synchronization criteria which are in the form of linear matrix inequality (LMI) are proved using a quadratic Lyapunov function. By means of MKY lemma the frequency domain criteria are further derived from the obtained LMIs. These frequency domain criteria are illustrated on the master-slave Chua's circuits with parameter mismatch so that the ranges of the parameters of Chua's circuit are analytically solved in the sense of the synchronization with finite L 2-gain by replacing singe-variable control. The illustrative examples verify that within the ranges of the parameters it is possible to synchronize the master-slave Chua's circuits up to a small synchronization error bound, even the qualitative behaviors of the slave circuit are different from that of the master one, such as the trajectory of the master circuit is chaotic and that of the slave divergent. The relation between the synchronization error bound and parameter mismatch is shown.

scholarly journals Error Bounds and Finite Termination for Constrained Optimization Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Wenling Zhao ◽  
Daojin Song ◽  
Bingzhuang Liu
Keyword(s):  
Constrained Optimization ◽  
Error Bound ◽  
Feasible Solution ◽  
Optimization Problems ◽  
Sufficient Conditions ◽  
Merit Function ◽  
Global Error Bound ◽  
Constrained Optimization Problems ◽  
Nonconvex Constrained Optimization ◽  
Necessary And Sufficient

We present a global error bound for the projected gradient of nonconvex constrained optimization problems and a local error bound for the distance from a feasible solution to the optimal solution set of convex constrained optimization problems, by using the merit function involved in the sequential quadratic programming (SQP) method. For the solution sets (stationary points set andKKTpoints set) of nonconvex constrained optimization problems, we establish the definitions of generalized nondegeneration and generalized weak sharp minima. Based on the above, the necessary and sufficient conditions for a feasible solution of the nonconvex constrained optimization problems to terminate finitely at the two solutions are given, respectively. Accordingly, the results in this paper improve and popularize existing results known in the literature. Further, we utilize the global error bound for the projected gradient with the merit function being computed easily to describe these necessary and sufficient conditions.

WPZI RINGS AND STRONG REGULARITY

2014 ◽  
Vol 0 (0) ◽  
Author(s):  
Junchao Wei
Keyword(s):  
Regular Ring ◽  
Strong Regularity ◽  
Strongly Regular

Abstract In this paper, we study the strong regularity of left SF rings and obtain the following results: Let R be a left SF ring. If R satisfies one of the following conditions, then R is a strongly regular ring: 1) R is a left WPZI ring; 2) R is a right WPZI ring; 3) R is a right weakly semicommutative ring; 4) R is a semicommutative ring; 5) R is a reversible ring.

scholarly journals On Accuracy of Improved χ 2-Approximations

2001 ◽  
Vol 8 (2) ◽  
pp. 401-414
Author(s):  
V. V. Ulyanov ◽  
Y. Fujikoshi
Keyword(s):  
Asymptotic Expansion ◽  
Error Bound ◽  
Sufficient Conditions ◽  
Scale Mixture ◽  
Bartlett Correction

Abstract For a statistic S whose distribution can be approximated by χ 2-distributions, there is a considerable interest in constructing improved χ 2-approximations. A typical approach is to consider a transformation T = T(S) based on the Bartlett correction or a Bartlett type correction. In this paper we consider two cases in which S is expressed as a scale mixture of a χ 2-variate or the distribution of S allows an asymptotic expansion in terms of χ 2-distributions. For these statistics, we give sufficient conditions for T to have an improved χ 2-approximation. Furthermore, we present a method for obtaining its error bound.

scholarly journals On strongly regular near-rings

1984 ◽  
Vol 27 (1) ◽  
pp. 61-64 ◽  
Author(s):  
Y. V. Reddy ◽  
C. V. L. N. Murty
Keyword(s):  
Strong Regularity ◽  
Strongly Regular

According to Mason [1] a right near-ring N is called (i) left (right) strongly regular if for every a there is an x in N such that a = xa2 (a = a2x) and (ii) left (right) regular if for every a there is an x in N such that a = xa2 (a = a2x) and a = axa. He proved that for a zerosymmetric near-ring with identity, the notions of left regularity, right regularity and left strong regularity are equivalent. The aim of this note is to prove that these three notions are equivalent for arbitrary near-rings. We also show that if N satisfies dec on iV-subgroups, then all the above four notions are equivalent.

scholarly journals Error Bound for Conic Inequality in Hilbert Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Jiangxing Zhu ◽  
Qinghai He ◽  
Jinchuan Lin
Keyword(s):  
Hilbert Space ◽  
Error Bound ◽  
Hilbert Spaces ◽  
Sufficient Conditions ◽  
Local Error ◽  
Local Error Bound ◽  
Local Error Bounds ◽  
Space Case ◽  
Vector Valued Functions ◽  
Vector Valued

We consider error bound issue for conic inequalities in Hilbert spaces. In terms of proximal subdifferentials of vector-valued functions, we provide sufficient conditions for the existence of a local error bound for a conic inequality. In the Hilbert space case, our result improves and extends some existing results on local error bounds.

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