We propose a nonmonotone adaptive trust region method based on simple conic model for unconstrained optimization. Unlike traditional trust region methods, the subproblem in our method is a simple conic model, where th...We propose a nonmonotone adaptive trust region method based on simple conic model for unconstrained optimization. Unlike traditional trust region methods, the subproblem in our method is a simple conic model, where the Hessian of the objective function is approximated by a scalar matrix. The trust region radius is adjusted with a new self-adaptive adjustment strategy which makes use of the information of the previous iteration and current iteration. The new method needs less memory and computational efforts. The global convergence and Q-superlinear convergence of the algorithm are established under the mild conditions. Numerical results on a series of standard test problems are reported to show that the new method is effective and attractive for large scale unconstrained optimization problems.展开更多
In this paper,an equivalency condition of nonsingularity in nonlinear semidefinite programming,which can be viewed as a generalization of the equivalency condition of nonsingularity for linearsemidefinite programming,...In this paper,an equivalency condition of nonsingularity in nonlinear semidefinite programming,which can be viewed as a generalization of the equivalency condition of nonsingularity for linearsemidefinite programming,is established under certain conditions of convexity.展开更多
基金Acknowledgements This work was supported by the National Natural Science Foundation of China （Grant No. 11171159）,the Specialized Research Fund of Doctoral Program of Higher Education of China （Grant No. 20103207110002）, the Fund for Innovative Program of Jiangsu Province （Grant No. CXLX12_0387）, CNPq-Brazil （Grant No. 301748/ 2011-0）, and the Research Fund of Pontifical Catholic University of Parana, Brazil.
文摘We propose a nonmonotone adaptive trust region method based on simple conic model for unconstrained optimization. Unlike traditional trust region methods, the subproblem in our method is a simple conic model, where the Hessian of the objective function is approximated by a scalar matrix. The trust region radius is adjusted with a new self-adaptive adjustment strategy which makes use of the information of the previous iteration and current iteration. The new method needs less memory and computational efforts. The global convergence and Q-superlinear convergence of the algorithm are established under the mild conditions. Numerical results on a series of standard test problems are reported to show that the new method is effective and attractive for large scale unconstrained optimization problems.
基金supported by the National Natural Science Foundation of China under Grant No. 10871098the Natural Science Fund of Jiangsu Province under Grant No. BK2009397the Innovation Fund of Youth of Fujian Province under Grant No. 2009J05003 and CNPq Brazil
文摘In this paper,an equivalency condition of nonsingularity in nonlinear semidefinite programming,which can be viewed as a generalization of the equivalency condition of nonsingularity for linearsemidefinite programming,is established under certain conditions of convexity.
