Superlinear Convergence of Primal-Dual Interior Point Algorithms for Nonlinear Programming

Superlinear Convergence of Primal-Dual Interior Point Algorithms for Nonlinear Programming

Local and superlinear convergence of a primal-dual interior point method for nonlinear semidefinite programming

In this paper, we consider a primal-dual interior point method for solving nonlinear semidefinite programming problems. We propose primal-dual interior point methods based on the unscaled and scaled Newton methods, which correspond to the AHO, HRVW/KSH/M and NT search directions in linear SDP problems. We analyze local behavior of our proposed methods and show their local and superlinear conver...

A Note on Superlinear Convergence of a Primal-dual Interior Point Method for Nonlinear Semi-definite Programming

We replace one of the assumptions (nondegeneracy assumption) in [9] to show that the main results in [9] still hold. We also provide a simple example to show that the new assumption is satisfied, while the original assumption is not satisfied, with other assumptions being satisfied. This example shows that the new assumption does not implied the original assumption.

A primal-dual interior point method for nonlinear semidefinite programming

In this paper, we consider a primal-dual interior point method for solving nonlinear semidefinite programming problems. By combining the primal barrier penalty function and the primal-dual barrier function, a new primal-dual merit function is proposed within the framework of the line search strategy. We show the global convergence property of our method.

Global convergence of a primal-dual interior-point method for nonlinear programming

Many recent convergence results obtained for primal-dual interior-point methods for nonlinear programming, use assumptions of the boundedness of generated iterates. In this paper we replace such assumptions by new assumptions on the NLP problem, develop a modification of a primal-dual interior-point method implemented in software package loqo and analyze convergence of the new method from any i...