Bento, G. C.
Cruz Neto, J. X.
Santos, P. S. M.
Souza, S. S.
We propose a weighting subgradient algorithm for solving multiobjective minimization problems on a nonempty closed convex subset of an Euclidean space. This method combines weighting technique and the classical projected subgradient method, using a divergent series steplength rule. Under the assumption of convexity, we show that the sequence generated by this method converges to a Pareto optimal point of the problem. Some numerical results are presented.
Based on the constrained variational inequality problem considered by Censor, Gibali and Reich (Numerical Algorithms, 2012), we propose, the constrained equilibrium problem (CEP), which consists in finding a point x* in the intersection of two nonempty, closed and convex subsets of an Euclidean space, C and D, such that x* is a solution of an equilibrium problem on C. In this work, an algorithm using projections is proposed to solve (CEP). Convergence properties of the algorithm are established under mild assumptions. Some numerical results are reported.
Brito, A. S.
Cruz Neto, J. X.
Santos, P. S. M.
Souza, S. S.
In this paper, we propose an algorithm for solving multiobjective minimization problems on nonempty closed convex subsets of the Euclidean space. The proposed method combines a reflection technique for obtaining a feasible point with a projected subgradient method. Under suitable assumptions, we show that the sequence generated using this method converges to a Pareto optimal point of the problem. We also present some numerical results. (C) 2016 Elsevier B.V. All rights reserved.
Cruz Neto, J. X.
Santos, P. S. M.
Silva, R. C. M.
Souza, J. C. O.
In this paper, we propose a Bregman regularized proximal point method for solving monotone equilibrium problems. Existence and uniqueness results as well as convergence of the sequence to a solution of an equilibrium problem is analyzed. We assume a coercivity condition on the Bregman function weaker than the one considered in the literature on equilibrium problems with Bregman regularization. Numerical experiments illustrate the efficiency of the method.
In this paper, we present an inexact version of the steepest descent method with Armijo's rule for multicriteria optimization in the Riemannian context given in Bento et al. (J. Optim. Theory Appl., 154: 88-107, 2012). Under mild assumptions on the multicriteria function, we prove that each accumulation point (if any) satisfies first-order necessary conditions for Pareto optimality. Moreover, assuming that the multicriteria function is quasi-convex and the Riemannian manifold has nonnegative curvature, we show full convergence of any sequence generated by the method to a Pareto critical point.
We consider the problem of general variational inequalities, GVI, with nonmonotone operator, in a finite dimensional space. We propose a method to solve GVI that at each iteration considers only one projection on an easy approximation of the constraint set, which is important from a practical point of view. We analyse the convergence of the algorithm under a weak cocoercivity condition, using variational metric analysis. Computational experience is reported and comparative analysis with other two algorithms is also given for the monotone case. (c) 2006 Elsevier Inc. All rights reserved.
Cruz Neto, J. X.
Lopes, J. O.
Santos, P. S. M.
Souza, J. C. O.
We present an interior proximal method for solving constrained nonconvex optimization problems where the objective function is given by the difference of two convex function (DC function). To this end, we consider a linearized proximal method with a proximal distance as regularization. Convergence analysis of particular choices of the proximal distance as second-order homogeneous proximal distances and Bregman distances are considered. Finally, some academic numerical results are presented for a constrained DC problem and generalized Fermat-Weber location problems.
The aim of this paper is to establish all self-dual lambda-constacyclic codes of length p(s) over the finite commutative chain ring R =3D F-p(m) + uF(p)(m), where p is a prime and u(2) =3D 0. If lambda =3D alpha+u beta for nonzero elements alpha, beta of F-p(m), the ideal < u > is the unique self-dual (alpha +u beta)-constacyclic codes. If lambda =3D gamma for some nonzero element gamma of F-p(m) we consider two cases of gamma. When gamma =3D gamma(-1), i.e., gamma =3D 1 or -1, we first obtain the dual of every cyclic code, a formula for the number of those cyclic codes and identify all self-dual cyclic codes. Then we use the ring isomorphism phi to carry over the results about cyclic accordingly to negacyclic codes. When gamma not equal gamma(-1), it is shown that < u > is the unique self-dual gamma-constacyclic code. Among other results, the number of each type of self-dual constacyclic code is obtained. (C) 2017 Elsevier B.V. All rights reserved.
Dinh, Hai Q.
Nguyen, Bac T.
Sriboonchitta, Songsak
For any odd prime p, negacyclic codes of length 4p(s) over the finite commutative chain ring F(p)m + uF(p)m are investigated. The algebraic structures of such codes are classified and completely determined. As an application, the number of codewords and the dual of each negacyclic code are obtained. Simpler structure of cyclic codes of length 4p(s) over F(p)m + uF(p)m is also noted. Among others, some self-dual negacyclic and cyclic codes of length 4p(s) over F(p)m + uF(p)m are provided. (C) 2018 Elsevier B.V. All rights reserved.
Dinh, H. Q.
Gaur, Atul
Singh, A. K.
Singh, Manoj Kumar
Yamaka, W.
In this research paper, the repeated-root constacyclic codes over the chain ring F-p(m) + uF(p)(m) are considered, where p is a prime and m > 0 is any integer. The b-symbol distance for prime power length, i.e. p(s) is also studied for any integer s > 0. The Hamming and symbol-pair distances of all delta-constacyclic codes have been thoroughly studied in [18], where delta is an unit in the ring F-p(m) + uF(p)(m) which is of the form zeta and phi + u phi, where 0 not equal phi, phi, zeta epsilon F-p(m). In this paper, the b-symbol distance of all such delta-constacyclic codes of prime power length is computed for 1 <=3D b <=3D b [p/2]. Furthermore, as an application, all MDS b-symbol constacyclic codes of length p(s) over F-p(m) + uF(p)(m) are established.