In this paper,the new SQP feasible descent algorithm for nonlinear constrained optimization problems presented,and under weaker conditions of relative,we proofed the new method still possesses global convergence and i...In this paper,the new SQP feasible descent algorithm for nonlinear constrained optimization problems presented,and under weaker conditions of relative,we proofed the new method still possesses global convergence and its strong convergence.The numerical results illustrate that the new methods are valid.展开更多
In this paper, a new superlinearly convergent algorithm for nonlinearly constrained optimization problems is presented. The search directions are directly computed by a few formulas, and neither quadratic programming ...In this paper, a new superlinearly convergent algorithm for nonlinearly constrained optimization problems is presented. The search directions are directly computed by a few formulas, and neither quadratic programming nor linear equation need to be sovled. Under mild assumptions, the new algorithm is shown to possess global and superlinear convergence.展开更多
The augmented Lagrangian method is a classical method for solving constrained optimization.Recently,the augmented Lagrangian method attracts much attention due to its applications to sparse optimization in compressive...The augmented Lagrangian method is a classical method for solving constrained optimization.Recently,the augmented Lagrangian method attracts much attention due to its applications to sparse optimization in compressive sensing and low rank matrix optimization problems.However,most Lagrangian methods use first order information to update the Lagrange multipliers,which lead to only linear convergence.In this paper,we study an update technique based on second order information and prove that superlinear convergence can be obtained.Theoretical properties of the update formula are given and some implementation issues regarding the new update are also discussed.展开更多
基金Supported by the NNSF of China(10231060)Supported by the Soft Science Foundation of Henan Province(082400430820)
文摘In this paper,the new SQP feasible descent algorithm for nonlinear constrained optimization problems presented,and under weaker conditions of relative,we proofed the new method still possesses global convergence and its strong convergence.The numerical results illustrate that the new methods are valid.
文摘In this paper, a new superlinearly convergent algorithm for nonlinearly constrained optimization problems is presented. The search directions are directly computed by a few formulas, and neither quadratic programming nor linear equation need to be sovled. Under mild assumptions, the new algorithm is shown to possess global and superlinear convergence.
基金Supported by National Natural Science Foundation of China(Grant Nos.10831006,11021101)by CAS(Grant No.kjcx-yw-s7)
文摘The augmented Lagrangian method is a classical method for solving constrained optimization.Recently,the augmented Lagrangian method attracts much attention due to its applications to sparse optimization in compressive sensing and low rank matrix optimization problems.However,most Lagrangian methods use first order information to update the Lagrange multipliers,which lead to only linear convergence.In this paper,we study an update technique based on second order information and prove that superlinear convergence can be obtained.Theoretical properties of the update formula are given and some implementation issues regarding the new update are also discussed.
