ﻻ يوجد ملخص باللغة العربية
We propose a semi-proximal augmented Lagrangian based decomposition method for convex composite quadratic conic programming problems with primal block angular structures. Using our algorithmic framework, we are able to naturally derive several well known augmented Lagrangian based decomposition methods for stochastic programming such as the diagonal quadratic approximation method of Mulvey and Ruszczy{n}ski. Moreover, we are able to derive novel enhancements and generalizations of these well known methods. We also propose a semi-proximal symmetric Gauss-Seidel based alternating direction method of multipliers for solving the corresponding dual problem. Numerical results show that our algorithms can perform well even for very large instances of primal block angular convex QP problems. For example, one instance with more than $300,000$ linear constraints and $12,500,000$ nonnegative variables is solved in less than a minute whereas Gurobi took more than 3 hours, and another instance {tt qp-gridgen1} with more than $331,000$ linear constraints and $986,000$ nonnegative variables is solved in about 5 minutes whereas Gurobi took more than 35 minutes.
In this paper, we aim to solve high dimensional convex quadratic programming (QP) problems with a large number of quadratic terms, linear equality and inequality constraints. In order to solve the targeted problems to a desired accuracy efficiently,
The augmented Lagrangian method (ALM) is a fundamental tool for solving the canonical convex minimization problem with linear constraints, and efficiently and easily how to implement the original ALM is affirmatively significant. Recently, He and Yua
In this paper we consider a class of convex conic programming. In particular, we propose an inexact augmented Lagrangian (I-AL) method for solving this problem, in which the augmented Lagrangian subproblems are solved approximately by a variant of Ne
In this paper, we aim to provide a comprehensive analysis on the linear rate convergence of the alternating direction method of multipliers (ADMM) for solving linearly constrained convex composite optimization problems. Under a certain error bound co
Shape-constrained convex regression problem deals with fitting a convex function to the observed data, where additional constraints are imposed, such as component-wise monotonicity and uniform Lipschitz continuity. This paper provides a unified frame