Publication Date: 2018
Optimization (10294945)67(8)pp. 1265-1286
In this paper, we propose a nonsmooth trust region algorithm for nonconvex optimization problems. The algorithm is based on notion of the Goldstein ϵ-subdifferential, which are subgradients computed in some neighbourhoods of a point. The proposed method contains a new quadratic model of the classical trust region method, in which the gradient vector is replaced by a quasisecant. Then we apply a combined approach based on the Cauchy point and the dog-leg methods in order to solve the obtained model. The global convergence is established under some suitable assumptions. Finally, the algorithm is implemented in the MATLAB environment and applied on some nonsmooth test problems. Numerical results on some small-scale and large-scale nonsmooth optimization test problems illustrate the efficiency of the proposed algorithm in the practical computation. © 2018, © 2018 Informa UK Limited, trading as Taylor & Francis Group.
Publication Date: 2015
Optimization (10294945)64(8)pp. 1669-1681
We show how to use intensively local cone approximations to obtain results in some fields of optimization theory as optimality conditions, constraint qualifications, mean value theorems and error bound. © 2014 Taylor & Francis.
Publication Date: 2006
Computers and Mathematics with Applications (08981221)51(9-10)pp. 1385-1394
In this paper, we consider notion of infine functions and we establish necessary and sufficient optimality conditions for a feasible solution of a multiobjective optimization problem involving mixed constraints (equality and inequality) to be an efficient or properly efficient solution. We also obtain duality theorems for Wolf type and Mond-Weir type duals under the generalized invexity assumptions. © 2006 Elsevier Ltd.
Publication Date: 2006
Journal of Optimization Theory and Applications (00223239)130(2)pp. 359-365
In this paper, we consider a generalization of convexity for nonsmooth multiobjective programming problems. We obtain sufficient optimality conditions under generalized (F, ρ)-convexity. © 2006 Springer Science+Business Media, Inc.
Publication Date: 2021
Positivity (13851292)25(2)pp. 701-729
In this paper, the robust approach (the worst case approach) for nonsmooth nonconvex optimization problems with uncertainty data is studied. First various robust constraint qualifications are introduced based on the concept of tangential subdifferential. Further, robust necessary and sufficient optimality conditions are derived in the absence of the convexity of the uncertain sets and the concavity of the related functions with respect to the uncertain parameters. Finally, the results are applied to obtain the necessary and sufficient optimality conditions for robust weakly efficient solutions in multiobjective programming problems. In addition, several examples are provided to illustrate the advantages of the obtained outcomes. © 2020, Springer Nature Switzerland AG.
Publication Date: 2007
Communications in Algebra (00927872)35(12)pp. 4277-4302
We introduce a new class of possibly infinite dimensional Lie algebras and study their structural properties. Examples of this new class of Lie algebras are finite dimensional simple Lie algebras containing a nonzero split torus, affine and extended affine Lie algebras. Our results generalize well-known properties of these examples.
Publication Date: 2015
Journal Of The Iranian Statistical Society (17264057)14(1)pp. 63-87
We consider a (n - κ + 1)-out-of-n system with exchangeable lifetimes of the components. The paper investigates the stochastic ordering properties of the residual lifetime of the system under condition that, at time t, at least (n - r + 1) components are alive. Some results are then extended to the case where the system has a coherent structure with exchangeable components.
Publication Date: 2011
Journal Of The Iranian Statistical Society (17264057)10(1)pp. 13-27
The dual generalized order statistics is a unified model which contains the well known decreasingly ordered random data such as (reversed ordered) order statistics and lower record values. In the present paper, some characterization results on the power function distribution based on the properties of dual generalized order statistics are provided. The results are proved without any restriction on the parameters of the model of dual GOS.
Publication Date: 2024
AIMS Mathematics (24736988)9(6)pp. 15837-15856
A Mixture of factor analyzer (MFA) model is a powerful tool to reduce the number of free parameters in high-dimensional data through the factor-analyzer technique based on the covariance matrices. This model also prepares an efficient methodology to determine latent groups in data. In this paper, we use an MFA model with a rich and flexible class of distributions called hidden truncation hyperbolic (HTH) distribution and a Bayesian structure with several computational benefits. The MFA based on the HTH family allows the factor scores and the error component can be skewed and heavy-tailed. Therefore, using the HTH family leads to the robustness of the MFA in modeling asymmetrical datasets with/without outliers. Furthermore, the HTH family, because of several desired properties, including analytical flexibility, provides steps in the estimation of parameters that are computationally tractable. In the present study, the advantages of MFA based on the HTH family have been discussed and the suitable efficiency of the introduced MFA model has been demonstrated by using real data examples and simulation. © 2024, American Institute of Mathematical Sciences. All rights reserved.
Publication Date: 2022
Journal of Applied Statistics (02664763)49(5)pp. 1305-1322
In this application note paper, we propose and examine the performance of a Bayesian approach for a homoscedastic nonlinear regression (NLR) model assuming errors with two-piece scale mixtures of normal (TP-SMN) distributions. The TP-SMN is a large family of distributions, covering both symmetrical/ asymmetrical distributions as well as light/heavy tailed distributions, and provides an alternative to another well-known family of distributions, called scale mixtures of skew-normal distributions. The proposed family and Bayesian approach provides considerable flexibility and advantages for NLR modelling in different practical settings. We examine the performance of the approach using simulated and real data. © 2020 Informa UK Limited, trading as Taylor & Francis Group.
Publication Date: 2019
Axioms (discontinued) (20751680)8(2)
In this paper, we examine the finite mixture (FM) model with a flexible class of two-piece distributions based on the scale mixtures of normal (TP-SMN) family components. This family allows the development of a robust estimation of FM models. The TP-SMN is a rich class of distributions that covers symmetric/asymmetric and light/heavy tailed distributions. It represents an alternative family to the well-known scale mixtures of the skew normal (SMSN) family studied by Branco and Dey (2001). Also, the TP-SMN covers the SMN (normal, t, slash, and contaminated normal distributions) as the symmetric members and two-piece versions of them as asymmetric members. A key feature of this study is using a suitable hierarchical representation of the family to obtain maximum likelihood estimates of model parameters via an EM-type algorithm. The performances of the proposed robust model are demonstrated using simulated and real data, and then compared to other finite mixture of SMSN models. © 2019 by the authors.
Publication Date: 2017
Communications in Statistics - Theory and Methods (1532415X)46(24)pp. 12356-12369
In this work, we study the maximum likelihood (ML) estimation problem for the parameters of the two-piece (TP) distribution based on the scale mixtures of normal (SMN) distributions. This is a family of skewed distributions that also includes the scales mixtures of normal class, and is flexible enough for modeling symmetric and asymmetric data. The ML estimates of the proposed model parameters are obtained via an expectation-maximization (EM)-type algorithm. © 2017 Taylor & Francis Group, LLC.
Publication Date: 2025
Journal of Algebra and its Applications (17936829)
We change Chermak-Delgado measure slightly so that it can be used for compact groups as well. Corresponding to this new measure, a lattice of open subgroups is obtained. Then we prove that if this lattice is non-empty in a compact group G, then G has a characteristic open abelian subgroup N such that [G: N] ≤ [G: A]2 for every abelian subgroup A G. This is a generalization of the well-known Chermak-Delgado Theorem. © 2026 World Scientific Publishing Company.
Publication Date: 2020
Bulletin Of The Malaysian Mathematical Sciences Society (01266705)43(3)pp. 2313-2320
It is proved that automorphism groups of all 2-groups of coclass 2 are 2-groups, except only three ones; for 2-groups of coclass 3, there are only 20 groups and exactly six infinite sequences of 2-groups whose automorphism groups are not 2-groups. © 2019, Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia.
Publication Date: 2018
Communications in Algebra (00927872)46(2)pp. 887-925
Kaplansky’s zero divisor conjecture (unit conjecture, respectively) states that for a torsion-free group G and a field &, the group ring &[G] has no zero divisors (has no units with supports of size greater than 1). In this paper, we study possible zero divisors and units in &[G] whose supports have size 3. For any field & and all torsion-free groups G, we prove that if αβ = 0 for some non-zero α,β∈&[G] such that |supp(α)| = 3, then |supp(β)|≥10. If & = &2 is the field with 2 elements, the latter result can be improved so that |supp(β)|≥20. This improves a result in Schweitzer [J. Group Theory, 16 (2013), no. 5, 667–693]. Concerning the unit conjecture, we prove that if αβ = 1 for some α,β∈&[G] such that |supp(α)| = 3, then |supp(β)|≥9. The latter improves a part of a result in Dykema et al. [Exp. Math., 24 (2015), 326–338] to arbitrary fields. © 2018 Taylor & Francis.
Publication Date: 2016
Ars Combinatoria (03817032)126pp. 301-310
Let ∗ be a binary graph operation. We call ∗ a Cayley operation if γ1 ∗ γ2 is a Cayley graph for any two Cayley graphs γ1 and γ2- In this paper, we prove that the cartesian, (categorical or tensor) direct and lexicographic products are Cayley operations. We also investigate the following question: Under what conditions on a binary graph operation ∗ and Cayley graphs γ1 ∗ γ2, the graph product γ1 ∗ γ2 is again a Cayley graph. The latter question is studied for the union, join (sum), replacement and zig-zag products of graphs.
Publication Date: 2013
International Journal Of Group Theory (22517669)2(4)pp. 17-20
A longstanding conjecture asserts that every finite nonabelian p-group admits a noninner automorphism of order p. Let G be a finite nonabelian p-group. It is known that if G is regular or of nilpotency class 2 or the commutator subgroup of G is cyclic, or G/Z(G) is powerful, then G has a noninner automorphism of order p leaving either the center Z(G) or the Frattini subgroup Φ(G) of G elementwise fixed. In this note, we prove that the latter noninner automorphism can be chosen so that it leaves Z(G) elementwise fixed. © 2013 University of Isfahan.
Publication Date: 2012
Journal of Algebra (00218693)357pp. 203-207
Let G be any non-abelian group and Z(G) be its center. The non-commuting graph Γ G of G is the simple graph whose vertex set is G\Z(G), with two vertices x and y adjacent whenever xy≠xy. We prove that if Γ G is isomorphic to the non-commuting graph of the alternating group A n (n≥4), then G≅A n. This result together with a recent one due to Solomon and Woldar gives a complete positive answer to a conjecture proposed in [A. Abdollahi, S. Akbari, H.R. Maimani, Non-commuting graph of a group, J. Algebra 298 (2006) 468-492]: If S is any finite non-abelian simple group such that Γ S≅Γ G for some group G, then G≅S. © 2012 Elsevier Inc.
Publication Date: 2010
Communications in Algebra (00927872)38(3)pp. 933-943
In this article we study left and right 4-Engel elements of a group. In particular, we prove that (a ab) is nilpotent of class at most 4, whenever a is of finite order and b±1 are right 4-Engel elements or a±1 are left 4-Engel elements and b is an arbitrary element of G. Furthermore, we prove that for any prime p and any element a of finite p-power order in a group G such that a±1 ∈ L4(G), a4, if p = 2, and ap, if p is an odd prime number, is in the Baer radical of G. © Taylor & Francis Group, LLC.
Publication Date: 2005
Journal of Pure and Applied Algebra (00224049)198(1-3)pp. 9-19
Let R be a ring and f(x1,..., xn) be a polynomial in noncommutative indeterminates x1,..., xn with coefficients from ℤ and zero constant. The ring R is said to be an f-ring if f(r1,..., rn) = 0 for all r1,..., rn of R and a virtually f-ring if for every n infinite subsets X1,..., Xn (not necessarily distinct) of R, there exist n elements r1 ∈ X1,...,rn ∈ Xn such that f(r1,..., rn) = 0. Let R* be the 'smallest' ring (in some sense) with identity containing R such that Char (R) = Char (R*). Then denote by ZR the subring generated by the identity of R* and denote by f̄R the image of f in ZR [x1,..., xn] (the ring of polynomials with coefficients in ZR in commutative indeterminates x1,..., xn). In this paper, we show that if R is a left primitive virtually f-ring such that f̄R ≠ 0, then R is finite. Using this result, we prove that an infinite semisimple virtually f-ring R is an f-ring, if the subring of ZR generated by the coefficients of f̄R is equal to ZR; and we also prove that if f(x) = ∑i=2n aixi + εx ∈ ℤ [x], where ε ∈ {-1, 1}, then every infinite virtually f-ring with identity is a commutative f-ring. Finally we show that a commutative Noetherian virtually f-ring R with identity is finite if the subring generated by the coefficients of f̄R is ZR. © 2004 Elsevier B.V. All rights reserved.
Publication Date: 2002
Bulletin of the Belgian Mathematical Society - Simon Stevin (13701444)9(2)pp. 205-215
In this paper, we consider some combinatorial conditions on infinite subsets of groups, and we obtain in terms of these conditions some characterizations of nilpotent-by-finite and finite-by-nilpotent groups on the class of finitely generated soluble groups.
Publication Date: 1999
Communications in Algebra (00927872)27(11)pp. 5633-5638
In this note we show that if G is a finitely generated soluble group, then every infinite subset of G contains two elements generating a nilpotent group of class at most k if and only if G is finite by a group in which every two generator subgroup is nilpotent of class at most k.
Publication Date: 2011
Georgian Mathematical Journal (1072947X)18(4)pp. 597-614
Recently, Huang, Li and O'Regan introduced a class of (scalar) generalized f-complementarity problems and three classes of variational inequalities in real Banach spaces for a fixed cone. Our aim is to introduce a vector case of their problems in the real topological vector spaces setting for a moving cone and to generalize their results even in the scalar case. © de Gruyter 2011.
Publication Date: 2011
Computers and Mathematics with Applications (08981221)61(7)pp. 1891-1897
In this paper, we introduce vector modular spaces and prove the existence of fixed points for generalized quasicontraction maps and discuss their uniqueness in these spaces. Our fixed point theorem, even in the case of modular spaces, extends the main result of Khamsi [M.A. Khamsi, Quasicontraction mappings in modular spaces without Δ2-condition, Fixed Point Theory and Applications 2008, 6 pages, ID 916187]. © 2011 Elsevier Ltd. All rights reserved.
Publication Date: 2009
Applied Mathematics Letters (18735452)22(7)pp. 1126-1129
In this work, we consider a generalized nonlinear variational-like inequality problem, in topological vector spaces, and, by using the KKM technique, we prove an existence theorem. Our result extends a theorem of Ahmad and Irfan [R. Ahmad, S.S. Irfan, On the generalized nonlinear variational-like inequality problems, Appl. Math. Lett. 19 (2006) 294-297]. © 2009 Elsevier Ltd. All rights reserved.
Publication Date: 2013
Environmental and Ecological Statistics (13528505)20(4)pp. 571-590
Adaptive two-stage sequential sampling (ATSSS) design was developed to observe more rare units and gain higher efficiency, in the sense of having a smaller variance estimator, than conventional sampling designs with equal effort for rare and spatially cluster populations. For certain rare populations, incorporating auxiliary variables into a sampling design can further improve the observation of rare units and increase efficiency. In this article, we develop regression-type estimators for ATSSS so that auxiliary variables can be incorporated into the ATSSS design when warranted. Simulation studies on two populations show that the regression-type estimators can significantly increase the efficiency of ATSSS and the detection of more rare units as compared to conventional sampling counterparts. Simulation of sampling of desert shrubs in Inner Mongolia (one of the two populations studied) showed that by incorporating a GIS auxiliary variable into ATSSS with the regression estimators resulted in a gain in efficiency over ATSSS without the auxiliary variable. Further, we found that the use of the GIS auxiliary variable in a conventional two-stage design with a regression estimator did not show a gain in efficiency. © 2013 Springer Science+Business Media New York.
