Zorana Luzanin - Academia.edu (original) (raw)

Papers by Zorana Luzanin

Research paper thumbnail of Convergence of the MRV Method at Singular Points 1

In this paper we give su-cient conditions for convergence of the Newton-like method with modiflca... more In this paper we give su-cient conditions for convergence of the Newton-like method with modiflcation of the right-hand-side vector (MRV) for a class of singular problems. The rate of convergence is sublin- ear. Numerical results are included witch agree well with the theoretically proven results.

Research paper thumbnail of Hybrid stochastic optimization algorithms with line search

A hybrid algorithm for solving unconstrained stochastic optimization problem is presented. The al... more A hybrid algorithm for solving unconstrained stochastic optimization problem is presented. The algorithm combines line search quasi Newton method, in particular BFGS method, with SA iterations. Details of computational implementa- tion and numerical results are given.

Research paper thumbnail of Convergence acceleration of a general Newton method for systems of nonlinear equations

Research paper thumbnail of On a Smoothing Quasi-Newton Method for Nonlinear Complementarity Problems

PAMM, 2003

Nonlinear complementarity problems (NCP) arise from optimization theory, engineering and economic... more Nonlinear complementarity problems (NCP) arise from optimization theory, engineering and economic applications. These problems are usually solved applying iterative methods to equivalent systems of nonlinear equations. We consider Jacobian smoothing quasi-Newton method for a semismooth equation reformulation of NCP based on Fisher-Burmeister function. Some numerical experiments of Jacobian smoothing method with modification of the right-handside vector are presented.

Research paper thumbnail of Newton-like method with modification of the right-hand-side vector

Mathematics of Computation, 2001

Abstract. This paper proposes a new Newton-like method which defines new iterates using a linear ... more Abstract. This paper proposes a new Newton-like method which defines new iterates using a linear system with the same coefficient matrix in each iterate, while the correction is performed on the right-hand-side vector of the Newton system. In this way a method is obtained ...

Research paper thumbnail of Practical Quasi-Newton algorithms for singular nonlinear systems

Numerical Algorithms, 2010

Quasi-Newton methods for solving singular systems of nonlinear equations are considered in this p... more Quasi-Newton methods for solving singular systems of nonlinear equations are considered in this paper. Singular roots cause a number of problems in implementation of iterative methods and in general deteriorate the rate of convergence. We propose two modifications of QN methods based on Newton's and Shamanski's method for singular problems. The proposed algorithms belong to the class of two-step iterations. Influence of iterative rule for matrix updates and the choice of parameters that keep iterative sequence within convergence region are empirically analyzed and some conclusions are obtained.

Research paper thumbnail of Jacobian smoothing Brown’s method for NCP

Nonlinear Analysis: Theory, Methods & Applications, 2009

Jacobian smoothing Brown's method for nonlinear complementarity problems (NCP) is studied in this... more Jacobian smoothing Brown's method for nonlinear complementarity problems (NCP) is studied in this paper. This method is a generalization of classical Brown's method. It belongs to the class of Jacobian smoothing methods for solving semismooth equations. Local convergence of the proposed method is proved in the case of a strictly complementary solution of NCP. Furthermore, a locally convergent hybrid method for general NCP is introduced. Some numerical experiments are also presented.

Research paper thumbnail of Iterative method with modification of the right-hand side vector for nonlinear complementarity problems

International Journal of Computer Mathematics, 2006

Research paper thumbnail of Newton-like method for nonlinear banded block diagonal system

Applied Mathematics and Computation, 2007

We present an efficient Newton-like method for solving systems of nonlinear equations with banded... more We present an efficient Newton-like method for solving systems of nonlinear equations with banded block diagonal structure. Such systems arise in economic models. The main idea of this method is to exploit the special structure of the Jacobian in a Newton-like method. The proposed algorithm uses an iterative method for calculation of the approximation of diagonal blocks in the Jacobian. Depending on dimensions of blocks significant reduction in computational cost is obtained and the algorithm can be easily parallelized. Local convergence of the proposed method is proved and some numerical results are presented.

Research paper thumbnail of Gauss–Newton-based BFGS method with filter for unconstrained minimization

Applied Mathematics and Computation, 2009

One class of the lately developed methods for solving optimization problems are filter methods. I... more One class of the lately developed methods for solving optimization problems are filter methods. In this paper we attached a multidimensional filter to the Gauss-Newton-based BFGS method given by Li and Fukushima [D. Li, M. Fukushima, A globally and superlinearly convergent Gauss-Newton-based BFGS method for symmetric nonlinear equations, SIAM Journal of Numerical Analysis 37(1) (1999) 152-172] in order to reduce the number of backtracking steps. The proposed filter method for unconstrained minimization problems converges globally under the standard assumptions. It can also be successfully used in solving systems of symmetric nonlinear equations. Numerical results show reasonably good performance of the proposed algorithm.

Research paper thumbnail of Convergence of the MRV Method at Singular Points 1

In this paper we give su-cient conditions for convergence of the Newton-like method with modiflca... more In this paper we give su-cient conditions for convergence of the Newton-like method with modiflcation of the right-hand-side vector (MRV) for a class of singular problems. The rate of convergence is sublin- ear. Numerical results are included witch agree well with the theoretically proven results.

Research paper thumbnail of Hybrid stochastic optimization algorithms with line search

A hybrid algorithm for solving unconstrained stochastic optimization problem is presented. The al... more A hybrid algorithm for solving unconstrained stochastic optimization problem is presented. The algorithm combines line search quasi Newton method, in particular BFGS method, with SA iterations. Details of computational implementa- tion and numerical results are given.

Research paper thumbnail of Convergence acceleration of a general Newton method for systems of nonlinear equations

Research paper thumbnail of On a Smoothing Quasi-Newton Method for Nonlinear Complementarity Problems

PAMM, 2003

Nonlinear complementarity problems (NCP) arise from optimization theory, engineering and economic... more Nonlinear complementarity problems (NCP) arise from optimization theory, engineering and economic applications. These problems are usually solved applying iterative methods to equivalent systems of nonlinear equations. We consider Jacobian smoothing quasi-Newton method for a semismooth equation reformulation of NCP based on Fisher-Burmeister function. Some numerical experiments of Jacobian smoothing method with modification of the right-handside vector are presented.

Research paper thumbnail of Newton-like method with modification of the right-hand-side vector

Mathematics of Computation, 2001

Abstract. This paper proposes a new Newton-like method which defines new iterates using a linear ... more Abstract. This paper proposes a new Newton-like method which defines new iterates using a linear system with the same coefficient matrix in each iterate, while the correction is performed on the right-hand-side vector of the Newton system. In this way a method is obtained ...

Research paper thumbnail of Practical Quasi-Newton algorithms for singular nonlinear systems

Numerical Algorithms, 2010

Quasi-Newton methods for solving singular systems of nonlinear equations are considered in this p... more Quasi-Newton methods for solving singular systems of nonlinear equations are considered in this paper. Singular roots cause a number of problems in implementation of iterative methods and in general deteriorate the rate of convergence. We propose two modifications of QN methods based on Newton's and Shamanski's method for singular problems. The proposed algorithms belong to the class of two-step iterations. Influence of iterative rule for matrix updates and the choice of parameters that keep iterative sequence within convergence region are empirically analyzed and some conclusions are obtained.

Research paper thumbnail of Jacobian smoothing Brown’s method for NCP

Nonlinear Analysis: Theory, Methods & Applications, 2009

Jacobian smoothing Brown's method for nonlinear complementarity problems (NCP) is studied in this... more Jacobian smoothing Brown's method for nonlinear complementarity problems (NCP) is studied in this paper. This method is a generalization of classical Brown's method. It belongs to the class of Jacobian smoothing methods for solving semismooth equations. Local convergence of the proposed method is proved in the case of a strictly complementary solution of NCP. Furthermore, a locally convergent hybrid method for general NCP is introduced. Some numerical experiments are also presented.

Research paper thumbnail of Iterative method with modification of the right-hand side vector for nonlinear complementarity problems

International Journal of Computer Mathematics, 2006

Research paper thumbnail of Newton-like method for nonlinear banded block diagonal system

Applied Mathematics and Computation, 2007

We present an efficient Newton-like method for solving systems of nonlinear equations with banded... more We present an efficient Newton-like method for solving systems of nonlinear equations with banded block diagonal structure. Such systems arise in economic models. The main idea of this method is to exploit the special structure of the Jacobian in a Newton-like method. The proposed algorithm uses an iterative method for calculation of the approximation of diagonal blocks in the Jacobian. Depending on dimensions of blocks significant reduction in computational cost is obtained and the algorithm can be easily parallelized. Local convergence of the proposed method is proved and some numerical results are presented.

Research paper thumbnail of Gauss–Newton-based BFGS method with filter for unconstrained minimization

Applied Mathematics and Computation, 2009

One class of the lately developed methods for solving optimization problems are filter methods. I... more One class of the lately developed methods for solving optimization problems are filter methods. In this paper we attached a multidimensional filter to the Gauss-Newton-based BFGS method given by Li and Fukushima [D. Li, M. Fukushima, A globally and superlinearly convergent Gauss-Newton-based BFGS method for symmetric nonlinear equations, SIAM Journal of Numerical Analysis 37(1) (1999) 152-172] in order to reduce the number of backtracking steps. The proposed filter method for unconstrained minimization problems converges globally under the standard assumptions. It can also be successfully used in solving systems of symmetric nonlinear equations. Numerical results show reasonably good performance of the proposed algorithm.