Author: "Jinyan Fan" / Journal: optimization methods and software - Searchworks@Jio Institute Digital Library Search Results

Author: Jinyan Fan and Haiyan Wang
Subjects: 021103 operations research, Control and Optimization, Applied Mathematics, Computer Science::Neural and Evolutionary Computation, Astrophysics::Instrumentation and Methods for Astrophysics, 0211 other engineering and technologies, 02 engineering and technology, Physics::Data Analysis, Statistics and Probability, 01 natural sciences, 010101 applied mathematics, Levenberg–Marquardt algorithm, symbols.namesake, Nonlinear system, Rate of convergence, Computer Science::Computational Engineering, Finance, and Science, Jacobian matrix and determinant, symbols, Applied mathematics, 0101 mathematics, Software, Mathematics
Abstract: In this paper, we study the convergence rate of the Levenberg-Marquardt (LM) method under the Holderian local error bound condition and the Holderian continuity of the Jacobian, which are more gene...
Published: 2019

Author: Ruixue Zhao, Jinyan Fan, and Jiawang Nie
Subjects: 021103 operations research, Control and Optimization, Applied Mathematics, MathematicsofComputing_NUMERICALANALYSIS, 0211 other engineering and technologies, 010103 numerical & computational mathematics, 02 engineering and technology, 01 natural sciences, Complementarity (physics), ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION, Applied mathematics, Polynomial optimization, Tensor, 0101 mathematics, Computer Science::Databases, Software, Eigenvalues and eigenvectors, Mathematics
Abstract: This paper proposes an algorithm for computing the maximum (or minimum) complementarity eigenvalues of tensors. We formulate this as proper polynomial optimization problems that can be efficiently ...
Published: 2018

Author: Jinyan Fan and Xin Zhao
Subjects: Sequence, 021103 operations research, Control and Optimization, Applied Mathematics, 0211 other engineering and technologies, 010103 numerical & computational mathematics, 02 engineering and technology, 01 natural sciences, Algebra, Complementarity (molecular biology), Tensor (intrinsic definition), Mathematics::Metric Geometry, Polynomial optimization, 0101 mathematics, Software, Mathematics
Abstract: In this paper, we study how to compute all real solutions of the tensor complimentary problem, if there are finite many ones. We formulate the problem as a sequence of polynomial optimization probl...
Published: 2018

Author: Ruixue Zhao and Jinyan Fan
Subjects: 021103 operations research, Control and Optimization, Applied Mathematics, 0211 other engineering and technologies, 010103 numerical & computational mathematics, 02 engineering and technology, Physics::Data Analysis, Statistics and Probability, 01 natural sciences, Levenberg–Marquardt algorithm, Nonlinear system, Merit function, 0101 mathematics, Algorithm, Software, Mathematics
Abstract: In this paper, we propose a new updating rule of the Levenberg–Marquardt LM parameter for the LM method for nonlinear equations. We show that the global complexity bound of the new LM algorithm is , that is, it requires at most iterations to derive the norm of the gradient of the merit function below the desired accuracy .
Published: 2016

Author: Na Lu and Jinyan Fan
Subjects: Trust region, Control and Optimization, Applied Mathematics, Computation, Mathematical analysis, MathematicsofComputing_NUMERICALANALYSIS, Zero (complex analysis), law.invention, Singular problems, symbols.namesake, Nonlinear system, Mathematics::Algebraic Geometry, Invertible matrix, law, ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION, Jacobian matrix and determinant, Convergence (routing), symbols, Software, Mathematics
Abstract: In this paper, we present a modified trust region algorithm for nonlinear equations with the trust region radii converging to zero. The algorithm calculates the Jacobian after every two computations of the step. It preserves the global convergence as the traditional trust region algorithms. Moreover, it converges nearly q-cubically under the local error bound condition, which is weaker than the nonsingularity of the Jacobian at a solution. Numerical results show that the algorithm is very efficient for both singular problems and nonsingular problems.
Published: 2014

Author: Ya-xiang Yuan and Jinyan Fan
Subjects: Hessian matrix, Trust region, Control and Optimization, Applied Mathematics, Mathematical analysis, MathematicsofComputing_NUMERICALANALYSIS, Local convergence, symbols.namesake, Nonlinear system, Monotone polygon, Rate of convergence, ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION, Convex optimization, symbols, Newton's method, Software, Mathematics
Abstract: In this paper, we propose a regularized Newton method for the system of monotone nonlinear equations. The regularization parameter is taken as the norm of the residual, and a correction step with little additional calculations is also computed to compensate for the shorter trial step due to the introduction of the regularization parameter. Under the local error bound condition which is weaker than nonsingularity, we show that the new regularized Newton method with correction has quadratic convergence. We also apply the new method to the unconstrained convex optimization problems which may have singular Hessian at the solutions and develop a globally convergent regularized Newton algorithm by using trust region technique. Numerical results show that the algorithm is very efficient and robust.
Published: 2013

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