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...

The convergence of primal and dual central paths associated to entropy and exponential functions, respectively, for semidefinite programming problem are studied in this paper. As an application, the proximal point method with the Kullback-Leibler distance applied to semidefinite programming problems is considered, and the convergence of primal and dual sequences is proved.

A new primal-dual algorithm is proposed for the minimization of non-convex objective functions subject to general inequality and linear equality constraints. The method uses a primal-dual trust-region model to ensure descent on a suitable merit function. Convergence is proved to second-order critical points from arbitrary starting points. Numerical results are presented for general quadratic pr...

In this paper, we present a new primal-dual interior-point algorithm for linear optimization based on a trigonometric kernel function. By simple analysis, we derive the worst case complexity for a large-update primal-dual interior-point method based on this kernel function. This complexity estimate improves a result from [1] and matches the one obtained in [2].

A practical warm-start procedure is described for the infeasible primal-dual interior-point method employed to solve the restricted master problem within the cutting-plane method. In contrast to the theoretical developments in this eld, the approach presented in this paper does not make the unrealistic assumption that the new cuts are shallow. Moreover, it treats systematically the case when a ...

For convex minimization we introduce an algorithm based on VU-space decomposition. The method uses a bundle subroutine to generate a sequence of approximate proximal points. When a primal-dual track leading to a solution and zero subgradient pair exists, these points approximate the primal track points and give the algorithm’s V, or corrector, steps. The subroutine also approximates dual track ...

23] C.L. Monma and A.J. Morton. Computational experimental with a dual aane variant of Karmarkar's method for linear programming. extension of Karmarkar type algorithm to a class of convex separable programming problems with global linear rate of convergence. Techni-28] J. Renegar. A polynomial-time algorithm based on Newton's method for linear programming. Implementing an interior point method...

The problem of establishing minimum-cost multicast connections in coded networks can be viewed as an optimization problem, and decentralized algorithms were proposed by Lun et al. to compute the optimal subgraph using the subgradient method on the dual problem. However, the convergence rate problem for these algorithms remains open. There are limited results in the literature on the convergence...

A fast Newton method is proposed for solving linear programs with a very large (≈ 10) number of constraints and a moderate (≈ 10) number of variables. Such linear programs occur in data mining and machine learning. The proposed method is based on the apparently overlooked fact that the dual of an asymptotic exterior penalty formulation of a linear program provides an exact least 2-norm solution...

In this survey, we give an overview of a technique used to design and analyze algorithms that provide approximate solutions to NP -hard problems in combinatorial optimization. Because of parallels with the primal-dual method commonly used in combinatorial optimization, we call it the primal-dual method for approximation algorithms. We show how this technique can be used to derive approximation ...