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.

We show that a modified variant of the interior point method can solve linear programs (LPs) whose coefficients are real numbers from a subring of the algebraic integers. By defining the encoding size of such numbers to be the bit size of the integers that represent them in the subring, we prove the modified algorithm runs in time polynomial in the encoding size of the input coefficients, the d...

Long step interior point methods in linear programming are some of the most e cient algorithms from a computational point of view. We prove polynomial complexity of a class of long step target following methods in a novel way, by introducing a new non-convex potential function and adapting the analysis framework of Jansen et al. [6, 7, 4]. The main advantage is that the new potential function h...

An infeasible interior-point algorithm for mixed symmetric cone linear complementarity problems is proposed. Using the machinery of Euclidean Jordan algebras and Nesterov-Todd search direction, the convergence analysis of the algorithm is shown and proved. Moreover, we obtain a polynomial time complexity bound which matches the currently best known iteration bound for infeasible interior-point ...

The paper considers a current example of Wächter and Biegler which is shown not to converge for the standard primal-dual interior-point method for nonlinear programming. Three possible solutions to the problem are derived and discussed, including shifting slack variables, a trust region method, and a modified barrier method. The paper then compares LOQO, a line-search interior-point code, with ...

Interior-point methods possess strong theoretical properties and have been successfully applied to a wide variety of linear and nonlinear programming applications. This paper presents a class of algorithms, based on interior-point methodology, for performing regularized maximum likelihood reconstructions on 3-D emission tomography data. The algorithms solve a sequence of subproblems that conver...

This article studies the linear multicommodity network flow problem. This kind of problem arises in a wide variety of contexts. A numerical implementation of the primal-dual interior-point method is designed to solve the problem. In the interior-point method, at each iteration, the corresponding linear problem, expressed as an augmented indefinite system, is solved by using the AINV algorithm c...

In this paper, we show that the moving directions of the primal-affine scaling method (with logarithmic barrier function), the dual-affine scaling method (with logarithmic barrier function), and the primal-dual interior point method are merely the Newton directions along three different algebraic "paths" that lead to a solution of the Karush-Kuhn-Tucker conditions of a given linear programming ...