In this paper, a trust-region algorithm is proposed for large-scale nonlinear equations, where the limited-memory BFGS (L-M-BFGS) update matrix is used in the trust-region subproblem to improve the effectiveness of the algorithm for large-scale problems. The global convergence of the presented method is established under suitable conditions. The numerical results of the test problems show that ...

We introduce a new trust-region method for unconstrained optimization where the radius update is computed using the model information at the current iterate rather than at the preceding one. The update is then performed according to how well the current model retrospectively predicts the value of the objective function at last iterate. Global convergence to rstand second-order critical points i...

The optimization of noisy or not exactly known functions is a common problem occuring in various applications as for instance in the task of experimental optimization. The traditional tool for the treatment of such problems is the method of Nelder-Mead (NM). In this paper an alternative method based on a trust region approach (TR) is ooered and compared to Nelder-Mead. On the standard collectio...

In this paper, we propose a trust region method for solving KKT systems arising from the variational inequality problem and the constrained optimization problem. The trust region subproblem is derived from reformulation of the KKT system as a constrained optimization problem and is solved by the truncated conjugate gradient method; meanwhile the variables remain feasible with respect to the con...

Abstract Gaussian Mixture Models are a powerful tool in Data Science and Statistics that mainly used for clustering density approximation. The task of estimating the model parameters is practice often solved by expectation maximization (EM) algorithm which has its benefits simplicity low per-iteration costs. However, EM converges slowly if there large share hidden information or overlapping clu...

We develop a trust-region method for minimizing the sum of smooth term (f) and nonsmooth (h), both which can be nonconvex. Each iteration our minimizes possibly nonconvex model (f + h) in trust region. The coincides with value subdifferential at center. establish global convergence to first-order stationary point when satisfies smoothness condition that holds, particular, it has Lipschitz-conti...