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Papers by luiz Carlos Matioli

Research paper thumbnail of Algorithms for the Nash Equilibrium Problem

a. Abstract: We discuss in this work algorithms for the Nash Equilibrium Problem - NEP, which can... more a. Abstract: We discuss in this work algorithms for the Nash Equilibrium Problem - NEP, which can be treated as a particular case of general Equilibrium Problem. Iusem and Nasri (1) introduce Augemented Lagrangian methods for solving finite dimensional equilibrium problems whose feasible sets are defined by convex inequalities, generalizing the proximal Augemented Lagrangian method for constrained optimization. Based on this work we present two metodologies to solve the NEP. In the smooth case, namely the functions involved in the problem are differentiable, we have to solve in each iteration of the methods a nonlinear and not differenciable system G(x) = 0, where G : R n ! R n . Both metodologies consist in a smoothing of the not differentiable term of G forming a new differentiable system G(x) = 0. The first metodology use the Newton method to solve G(x) = 0. We show that the Newton direction is well defined and the convergence results shown by Iusem and Nasri are still valid. The...

Research paper thumbnail of New Optimization Algorithms for Structural Reliability Analysis

Cmes-computer Modeling in Engineering & Sciences, 2012

Research paper thumbnail of A new algorithm for clustering based on kernel density estimation

Journal of Applied Statistics, Jan 12, 2017

Research paper thumbnail of Augmented Lagrangian applied to convex quadratic problems

Applied Mathematics and Computation, Jul 1, 2008

Research paper thumbnail of Métodos De Lagrangeano Aumentado e Gradiente Espectral Projetado Aplicados Na Resolução Do Problema Do Despacho Hidrotérmico

Research paper thumbnail of Generalized Graph Product and its Application on Generating Solutions of the Millennium n-Queens Problem

Research paper thumbnail of Least square method and bilevel programming applied to works selection in the distribution system

Research paper thumbnail of A short note on a generalization of the Givens transformation

Computers & mathematics with applications, Aug 1, 2013

Research paper thumbnail of A new family of penalties for augmented Lagrangian methods

Numerical Linear Algebra With Applications, Dec 1, 2008

Research paper thumbnail of Augmented Lagrangian algorithms for solving the continuous nonlinear resource allocation problem

European Journal of Operational Research, May 1, 2022

Research paper thumbnail of A numerical algorithm for finding solutions of a generalized Nash equilibrium problem

Computational Optimization and Applications, Apr 8, 2011

Research paper thumbnail of Exponential augmented Lagrangian methods for equilibrium problems

Optimization Methods & Software, Apr 22, 2020

Research paper thumbnail of Methodology to Works Prioritization in the Distribution System

This paper proposes a work selection methodology to the medium-voltage distribution system aiming... more This paper proposes a work selection methodology to the medium-voltage distribution system aiming to adequate the reliability continuity indexes DEC and FEC (it corresponds to the English abbreviations SAIDI and SAIFI, respectively) to the limits defined by the Brazilian regulatory agency. This mathematical methodology is based on the optimization program and the works selection problem will be modeled and simulated

Research paper thumbnail of Uma nova metodologia para construção de funções de penalização para algoritmos de lagrangeano aumentado

Research paper thumbnail of TreeKDE: clustering multivariate data based on decision tree and using one-dimensional kernel density estimation

Journal of Applied Statistics

Research paper thumbnail of AdditiveClusterKDE: Um algoritmo para clusterização baseado no estimador de densidade kernel multivariado

Proceeding Series of the Brazilian Society of Computational and Applied Mathematics, 2021

Resumo. Nesse artigo apresentamos um algoritmo para clusterização baseado na estimativa de densid... more Resumo. Nesse artigo apresentamos um algoritmo para clusterização baseado na estimativa de densidade kernel multivariada. O algoritmo denominado AdditiveClusterKDE é centrado na múltipla otimização da função do Estimador de Densidade Kernel com kernel Gaussiano multivariado. O algoritmo proposto tem a vantagem de não exigir a priori o número de clusters, além disso, ele é simples, fácil de implementar, bem definido e para em um número finito de etapas, ou seja, sempre converge independentemente do conjunto de dados a ser agrupado. Implementamos o algoritmo no software R e fizemos experimentos numéricos com dados de problemas práticos obtidos na literatura e dados produzidos de forma sintética para uma melhor abrangência das potencialidades do algoritmo. Resultados preliminares indicam que o algoritmo AdditiveClusterKDE é competitivo quando comparado com os algoritmos K-means e PdfCluster.

Research paper thumbnail of Identification, Tracking and Nowcasting of Electrical Storms Using Numerical Methods

This research presents a method of identification, tracking and nowcasting of electrical storms b... more This research presents a method of identification, tracking and nowcasting of electrical storms based on lightning clustering and spatial/temporal connections of electrical centers detected. During the process, different meteorological variables are calculated and then projected one hour ahead by data extrapolation technique. The validation of the proposed methodology is made by comparing the observed data with the prediction held. The methodology is validated and applied on a region covering the more important brazilian electric power transmission line, highly vulnerable to weather conditions, especially affected by lightning strokes. Practical examples are presented in order to view the product of the proposed system, where two different situations are analyzed.

Research paper thumbnail of Least square method and bilevel programming applied to works selection in the distribution system

In this paper we propose a work selection methodology to the medium-voltage distribution system a... more In this paper we propose a work selection methodology to the medium-voltage distribution system aiming to adequate the reliability continuity index (DEC) to the limits defined by the regulatory agency. The Portuguese abbreviation DEC corresponds to the English abbreviation SAIDI (System Average Interruption duration Index). That step comes after the technical and financial classification phase of the works. Based on minimum square method concept and using bilevel programming, it presents a mathematical treatment and applies this methodology in part of COPELs annual works planning program. COPEL is a Brazilian utility company of generation, distribution and commercialization of electricity.

Research paper thumbnail of A multiplier method with a class of penalty functions for convex programming ‡

We consider a class of augmented Lagrangian methods for solving convex programming problems with ... more We consider a class of augmented Lagrangian methods for solving convex programming problems with inequality constraints. This class involves a family of penalty functions and specific values of parameters p, q, ỹ ∈ R and c > 0. The penalty family includes the classical modified barrier and the exponential function. The associated proximal method for solving the dual problem is also considered. Convergence results are shown, specifically we prove that any limit point of the primal and the dual sequence generated by the algorithms are optimal solutions of the primal and dual problem respectively.

Research paper thumbnail of M ´ Etodo De Intersec ¸ ˜ Ao De Esferas Aplicado Ao C ´ Alculo De Estruturas De Prote ´

Research paper thumbnail of Algorithms for the Nash Equilibrium Problem

a. Abstract: We discuss in this work algorithms for the Nash Equilibrium Problem - NEP, which can... more a. Abstract: We discuss in this work algorithms for the Nash Equilibrium Problem - NEP, which can be treated as a particular case of general Equilibrium Problem. Iusem and Nasri (1) introduce Augemented Lagrangian methods for solving finite dimensional equilibrium problems whose feasible sets are defined by convex inequalities, generalizing the proximal Augemented Lagrangian method for constrained optimization. Based on this work we present two metodologies to solve the NEP. In the smooth case, namely the functions involved in the problem are differentiable, we have to solve in each iteration of the methods a nonlinear and not differenciable system G(x) = 0, where G : R n ! R n . Both metodologies consist in a smoothing of the not differentiable term of G forming a new differentiable system G(x) = 0. The first metodology use the Newton method to solve G(x) = 0. We show that the Newton direction is well defined and the convergence results shown by Iusem and Nasri are still valid. The...

Research paper thumbnail of New Optimization Algorithms for Structural Reliability Analysis

Cmes-computer Modeling in Engineering & Sciences, 2012

Research paper thumbnail of A new algorithm for clustering based on kernel density estimation

Journal of Applied Statistics, Jan 12, 2017

Research paper thumbnail of Augmented Lagrangian applied to convex quadratic problems

Applied Mathematics and Computation, Jul 1, 2008

Research paper thumbnail of Métodos De Lagrangeano Aumentado e Gradiente Espectral Projetado Aplicados Na Resolução Do Problema Do Despacho Hidrotérmico

Research paper thumbnail of Generalized Graph Product and its Application on Generating Solutions of the Millennium n-Queens Problem

Research paper thumbnail of Least square method and bilevel programming applied to works selection in the distribution system

Research paper thumbnail of A short note on a generalization of the Givens transformation

Computers & mathematics with applications, Aug 1, 2013

Research paper thumbnail of A new family of penalties for augmented Lagrangian methods

Numerical Linear Algebra With Applications, Dec 1, 2008

Research paper thumbnail of Augmented Lagrangian algorithms for solving the continuous nonlinear resource allocation problem

European Journal of Operational Research, May 1, 2022

Research paper thumbnail of A numerical algorithm for finding solutions of a generalized Nash equilibrium problem

Computational Optimization and Applications, Apr 8, 2011

Research paper thumbnail of Exponential augmented Lagrangian methods for equilibrium problems

Optimization Methods & Software, Apr 22, 2020

Research paper thumbnail of Methodology to Works Prioritization in the Distribution System

This paper proposes a work selection methodology to the medium-voltage distribution system aiming... more This paper proposes a work selection methodology to the medium-voltage distribution system aiming to adequate the reliability continuity indexes DEC and FEC (it corresponds to the English abbreviations SAIDI and SAIFI, respectively) to the limits defined by the Brazilian regulatory agency. This mathematical methodology is based on the optimization program and the works selection problem will be modeled and simulated

Research paper thumbnail of Uma nova metodologia para construção de funções de penalização para algoritmos de lagrangeano aumentado

Research paper thumbnail of TreeKDE: clustering multivariate data based on decision tree and using one-dimensional kernel density estimation

Journal of Applied Statistics

Research paper thumbnail of AdditiveClusterKDE: Um algoritmo para clusterização baseado no estimador de densidade kernel multivariado

Proceeding Series of the Brazilian Society of Computational and Applied Mathematics, 2021

Resumo. Nesse artigo apresentamos um algoritmo para clusterização baseado na estimativa de densid... more Resumo. Nesse artigo apresentamos um algoritmo para clusterização baseado na estimativa de densidade kernel multivariada. O algoritmo denominado AdditiveClusterKDE é centrado na múltipla otimização da função do Estimador de Densidade Kernel com kernel Gaussiano multivariado. O algoritmo proposto tem a vantagem de não exigir a priori o número de clusters, além disso, ele é simples, fácil de implementar, bem definido e para em um número finito de etapas, ou seja, sempre converge independentemente do conjunto de dados a ser agrupado. Implementamos o algoritmo no software R e fizemos experimentos numéricos com dados de problemas práticos obtidos na literatura e dados produzidos de forma sintética para uma melhor abrangência das potencialidades do algoritmo. Resultados preliminares indicam que o algoritmo AdditiveClusterKDE é competitivo quando comparado com os algoritmos K-means e PdfCluster.

Research paper thumbnail of Identification, Tracking and Nowcasting of Electrical Storms Using Numerical Methods

This research presents a method of identification, tracking and nowcasting of electrical storms b... more This research presents a method of identification, tracking and nowcasting of electrical storms based on lightning clustering and spatial/temporal connections of electrical centers detected. During the process, different meteorological variables are calculated and then projected one hour ahead by data extrapolation technique. The validation of the proposed methodology is made by comparing the observed data with the prediction held. The methodology is validated and applied on a region covering the more important brazilian electric power transmission line, highly vulnerable to weather conditions, especially affected by lightning strokes. Practical examples are presented in order to view the product of the proposed system, where two different situations are analyzed.

Research paper thumbnail of Least square method and bilevel programming applied to works selection in the distribution system

In this paper we propose a work selection methodology to the medium-voltage distribution system a... more In this paper we propose a work selection methodology to the medium-voltage distribution system aiming to adequate the reliability continuity index (DEC) to the limits defined by the regulatory agency. The Portuguese abbreviation DEC corresponds to the English abbreviation SAIDI (System Average Interruption duration Index). That step comes after the technical and financial classification phase of the works. Based on minimum square method concept and using bilevel programming, it presents a mathematical treatment and applies this methodology in part of COPELs annual works planning program. COPEL is a Brazilian utility company of generation, distribution and commercialization of electricity.

Research paper thumbnail of A multiplier method with a class of penalty functions for convex programming ‡

We consider a class of augmented Lagrangian methods for solving convex programming problems with ... more We consider a class of augmented Lagrangian methods for solving convex programming problems with inequality constraints. This class involves a family of penalty functions and specific values of parameters p, q, ỹ ∈ R and c > 0. The penalty family includes the classical modified barrier and the exponential function. The associated proximal method for solving the dual problem is also considered. Convergence results are shown, specifically we prove that any limit point of the primal and the dual sequence generated by the algorithms are optimal solutions of the primal and dual problem respectively.

Research paper thumbnail of M ´ Etodo De Intersec ¸ ˜ Ao De Esferas Aplicado Ao C ´ Alculo De Estruturas De Prote ´