An interior-point Lagrangian decomposition method for separable convex optimization
نویسنده
چکیده
In this paper we propose a distributed algorithm for solving large-scale separable convex problems using Lagrangian dual decomposition and the interior-point framework. By adding self-concordant barrier terms to the ordinary Lagrangian we prove under mild assumptions that the corresponding family of augmented dual functions is self-concordant. This makes it possible to efficiently use the Newton method for tracing the central path. We show that the new algorithm is globally convergent and highly parallelizable and thus it is suitable for solving large-scale separable convex problems.
منابع مشابه
Solving Quadratic Multicommodity Problems through an Interior-Point Algorithm
Standard interior-point algorithms usually show a poor performance when applied to multicommodity network flows problems. A recent specialized interior-point algorithm for linear multicommodity network flows overcame this drawback, and was able to efficiently solve large and difficult instances. In this work we perform a computational evaluation of an extension of that specialized algorithm for...
متن کاملAn Interior Point Algorithm for Solving Convex Quadratic Semidefinite Optimization Problems Using a New Kernel Function
In this paper, we consider convex quadratic semidefinite optimization problems and provide a primal-dual Interior Point Method (IPM) based on a new kernel function with a trigonometric barrier term. Iteration complexity of the algorithm is analyzed using some easy to check and mild conditions. Although our proposed kernel function is neither a Self-Regular (SR) fun...
متن کاملOn the Proximal Jacobian Decomposition of ALM for Multiple-Block Separable Convex Minimization Problems and Its Relationship to ADMM
The augmented Lagrangian method (ALM) is a benchmark for solving convex minimization problems with linear constraints. When the objective function of the model under consideration is representable as the sum of some functions without coupled variables, a Jacobian or Gauss-Seidel decomposition is often implemented to decompose the ALM subproblems so that the functions’ properties could be used m...
متن کاملAn Asymmetric Proximal Decomposition Method for Convex Programming with Linearly Coupling Constraints
The problems studied are the separable variational inequalities with linearly coupling constraints. Some existing decomposition methods are very problem specific, and the computation load is quite costly. Combining the ideas of proximal point algorithm PPA and augmented Lagrangian method ALM , we propose an asymmetric proximal decomposition method AsPDM to solve a wide variety separable problem...
متن کاملAn Inexact Perturbed Path-Following Method for Lagrangian Decomposition in Large-Scale Separable Convex Optimization
This paper studies an inexact perturbed path-following algorithm in the framework of Lagrangian dual decomposition for solving large-scale separable convex programming problems. Unlike the exact versions considered in the literature, we propose to solve the primal subproblems inexactly up to a given accuracy. This leads to an inexactness of the gradient vector and the Hessian matrix of the smoo...
متن کامل