The augmented Lagrangian method with full Jacobian decomposition and logarithmic-quadratic proximal regularization for multiple-block separable convex programming
نویسندگان
چکیده
منابع مشابه
On Full Jacobian Decomposition of the Augmented Lagrangian Method for Separable Convex Programming
The augmented Lagrangian method (ALM) is a benchmark for solving a convex minimization model with linear constraints. We consider the special case where the objective is the sum of m functions without coupled variables. For solving this separable convex minimization model, it is usually required to decompose the ALM subproblem at each iteration into m smaller subproblems, each of which only inv...
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The augmented Lagrangian method (ALM) is fundamental for solving convex programming problems with linear constraints. The proximal version of ALM, which regularizes ALM’s subproblem over the primal variable at each iteration by an additional positive-definite quadratic proximal term, has been well studied in the literature. In this paper, we show that it is not necessary to employ a positive-de...
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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...
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e-mail: [email protected] Abstract. The purpose of this paper is threefold. First we propose splitting schemes for reformulating non-separable problems as block-separable problems. Second we show that the Lagrangian dual of a block-separable mixed-integer all-quadratic program (MIQQP) can be formulated as an eigenvalue optimization problem keeping the block-separable structure. Finall...
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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 Newto...
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ژورنال
عنوان ژورنال: The SMAI journal of computational mathematics
سال: 2018
ISSN: 2426-8399
DOI: 10.5802/smai-jcm.30