Nonlinear stepsize control, trust regions and regularizations for unconstrained optimization
نویسنده
چکیده
A general class of algorithms for unconstrained optimization is introduced, which subsumes the classical trust-region algorithm and two of its newer variants, as well as the cubic and quadratic regularization methods. A unified theory of global convergence to first-order critical points is then described for this class. An extension to projection-based trust-region algorithms for nonlinear optimization over convex sets is also presented.
منابع مشابه
Numerical Experience with a Class of Trust-Region Algorithms for Unconstrained Smooth Optimization
In this paper we investigate the numerical performance of trust-region algorithms in which the trust-region radius is updated by a nonlinear rule according with the quality of the models. This class of algorithms fits into the Nonlinear Stepsize Control framework recently proposed by Toint (Optimization Methods and Software 28: 82–95, 2013). The nonlinear control of the trust-region radius is c...
متن کاملA Trust-region Method using Extended Nonmonotone Technique for Unconstrained Optimization
In this paper, we present a nonmonotone trust-region algorithm for unconstrained optimization. We first introduce a variant of the nonmonotone strategy proposed by Ahookhosh and Amini cite{AhA 01} and incorporate it into the trust-region framework to construct a more efficient approach. Our new nonmonotone strategy combines the current function value with the maximum function values in some pri...
متن کاملA limited memory adaptive trust-region approach for large-scale unconstrained optimization
This study concerns with a trust-region-based method for solving unconstrained optimization problems. The approach takes the advantages of the compact limited memory BFGS updating formula together with an appropriate adaptive radius strategy. In our approach, the adaptive technique leads us to decrease the number of subproblems solving, while utilizing the structure of limited memory quasi-Newt...
متن کاملSolving the Unconstrained Optimization Problems Using the Combination of Nonmonotone Trust Region Algorithm and Filter Technique
In this paper, we propose a new nonmonotone adaptive trust region method for solving unconstrained optimization problems that is equipped with the filter technique. In the proposed method, the various nonmonotone technique is used. Using this technique, the algorithm can advantage from nonmonotone properties and it can increase the rate of solving the problems. Also, the filter that is used in...
متن کاملA Filter-Trust-Region Method for Unconstrained Optimization
A new filter-trust-region algorithm for solving unconstrained nonlinear optimization problems is introduced. Based on the filter technique introduced by Fletcher and Leyffer, it extends an existing technique of Gould, Leyffer, and Toint [SIAM J. Optim., 15 (2004), pp. 17–38] for nonlinear equations and nonlinear least-squares to the fully general unconstrained optimization problem. The new algo...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Optimization Methods and Software
دوره 28 شماره
صفحات -
تاریخ انتشار 2013