PRACTICAL ALGORITHMS FOR LARGE SCALE CONVEX COMPOSITE CONIC PROGRAMMING PROBLEM

Abstract

We design and implement specialized algorithms for solving various large scale optimization problems arising from literature. We first study large scale generalized distance weighted discrimination model, where we design a scalable and robust algorithm for solving it. Secondly, we propose a semi-proximal augmented Lagrangian based decomposition method for convex composite quadratic conic programming problems with primal block angular structures. We can naturally derive several well-known augmented Lagrangian based decomposition methods for stochastic programming such as the diagonal quadratic approximation method of Mulvey and Ruszczyński. We also propose a semi-proximal symmetric Gauss-Seidel (sGS) based alternating direction method of multipliers for solving the corresponding dual problem. Lastly, we design an inexact proximal augmented Lagrangian based decomposition methods for convex composite conic programming problems with dual block angular structures. The algorithmic framework is based on the sGS decomposition theorem, and its advantage is that the computation of subproblems are easy to be parallelized.