Trust-region method optimization

In conclusion, the trust region method is more intuitive than the RF model and provides a more natural step control. On the other hand, RF optimization avoids the solution of one set of linear equations, which is important when the number of variables is large. 

The basic structure of an iterative local optimization algorithm is one of greedy descent . It is based on one of the following two algorithmic frameworks line-search or trust-region methods. Both are found throughout the literature and in software packages and are essential components of effective... 

The idea in trust-region methods - the origin of the quadratic optimization subproblem in step 2 above - is to determine the vector s on the basis of the size of region within which the quadratic functional approximation can be trusted (i.e., is reasonable). The quality of the quadratic approximation can be assessed from the following ratio ... 

Thekale A Trust-region methods for simulation based nonlinear optimization, Doktorarbeit, 2011, Friedrich-Alexander-Universitat Erlangen-Niimberg (FAU). 

To solve the equations of problem P ), the optimization algorithms used are Levenberg-Marquardt and Trust-Region procedures. These methods enable computation of the solution by using the Jacobian matrix and the Hessian matrix (or its approximation) related to the objective function E(Y) [57]. 

Problem Type Large bound-constrained optimization problems Method Trust region Newton method... 

We now turn to a method closely related to the Levenberg-Marquardt trust-region scheme. Rather than searching for the global optimizer of the restricted local model, we seek to trace out on the second-order model surface the steepest-descent path as defined by the equation... 

LANCELOT Philippe Toint pht raath.fundp.ac.be Various Newton methods for constrained and unconstrained nonlinear optimization, specializing in laige-scale problems and including a trust-region Newton method and an algorithm for nonlinear least squares that exploits partial separability... 

This kind of algorithms firstly constructs a model function (trust region) mk whose behavior near the current solution Xk is similar to that of the actual objective function/. Then, these methods choose the step and the direction to find the approximate optimizer of the model in this trust region. 

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