We introduce and analyze a trust–region sequential quadratic programming (SQP) method for the solution of smooth equality constrained optimization problems, which allows the inexact and hence iterative solution of linear systems. Iterative solution of linear systems is important in large-scale applications, such as optimization problems with partial differential equation constraints, where dire...

In this paper we propose a filter-trust-region algorithm for solving nonlinear optimization problems with simple bounds. It extends the technique of Gould, Sainvitu and Toint [15] designed for unconstrained optimization. The two main ingredients of the method are a filter-trust-region algorithm and the use of a gradient-projection method. The algorithm is shown to be globally convergent to at l...

In this talk, we present a trust region method for solving equality constrained optimization problems, which is motivated by the famous augmented Lagrangian function. It is different from standard augmented Lagrangian methods where the augmented Lagrangian function is minimized at each iteration. This method, for fixed Lagrange multiplier and penalty parameters, tries to minimize an approximate...

We present a non-smooth optimization technique for non-convex maximum eigenvalue functions and for non-smooth functions which are infinite maxima of eigenvalue functions. We prove global convergence of our method in the sense that for an arbitrary starting point, every accumulation point of the sequence of iterates is critical. The method is tested on several problems in feedback control synthe...

The analog-integrated circuits industry is exerting increasing pressure to shorten the analog circuit design time. This pressure is put primarily on the analog circuit designers that in turn demand automated circuit design tools evermore vigorously. Such tools already exist in the form of circuit optimization software packages but they all suffer a common ailment — slow convergence. Even taking...

The well-known symmetric rank-one trust-region method—where the Hessian approximation is generated by the symmetric rank-one update—is generalized to the problem of minimizing a real-valued function over a d-dimensional Riemannian manifold. The generalization relies on basic differential-geometric concepts, such as tangent spaces, Riemannian metrics, and the Riemannian gradient, as well as on t...

The main purpose of this paper is to show that linear least squares methods based on bidiagonalization, namely the LSQR algorithm, can be used for generation of trust region path. This property is a basis for an inexact trust region method which uses the LSQR algorithm for direction determination. This method is very efficient for large sparse nonlinear least squares as it is supported by numer...

The estimation of multivariate GARCH time series models is a difficult task mainly due to the significant overparameterization exhibited by the problem and usually referred to as the “curse of dimensionality”. For example, in the case of the VEC family, the number of parameters involved in the model grows as a polynomial of order four on the dimensionality of the problem. Moreover, these parame...

In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: a b s t r a c t In this paper, we propose a BFGS trust-region method for solving symmetric nonlinear equations. The global c...

With the emergence of big data, there has been a growing interest in optimization routines that lead to faster convergence of Logistic Regression (LR). Among many optimization methods such as Gradient Descent, Quasi-Newton, Conjugate Gradient, etc., the Trust-region based truncated Newton method (TRON) algorithm has been shown to converge the fastest. The TRON algorithm also forms an important ...