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Semi-proximal Augmented Lagrangian-Based Decomposition Methods for Primal Block-Angular Convex Composite Quadratic Conic Programming Problems

We first propose a semi-proximal augmented Lagrangian-based decomposition method to directly solve the primal form of a convex composite quadratic conic-programming problem with a primal block-angular structure. 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 Ruszczyński. Although it is natural to develop an augmented Lagrangian decomposition algorithm based on the primal problem, here, we demonstrate that it is, in fact, numerically more economical to solve the dual problem by an appropriately designed decomposition algorithm. In particular, we propose a semi-proximal symmetric Gauss–Seidel-based alternating direction method of multipliers (sGS-ADMM) for solving the corresponding dual problem. Numerical results show that our dual-based sGS-ADMM algorithm can very efficiently solve some very large instances of primal block-angular convex quadratic-programming problems. For example, one instance with more than 300,000 linear constraints and 12.5 million nonnegative variables is solved to the accuracy of 10-5 in the relative KKT residual in less than a minute on a modest desktop computer.

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Informasi Detail

Judul Seri

INFORMS JOURNAL ON OPTIMIZATION; Vol.3 No.3 Summer 2021

No. Panggil

-

Penerbit

: .,

Deskripsi Fisik

p. 254 - 277

Bahasa

English

ISBN/ISSN

-

Klasifikasi

NONE

Tipe Isi

-

Tipe Media

-

Tipe Pembawa

-

Edisi

-

Subjek

ADMM
DIAGONAL QUADRATIC APPROXIMATION METHOD
SYMMETRIC GAUSS-SEIDEL DECOMPOSITION
SEMI-PROXIMAL AUGMENTED LAGRANGIAN METHOD
PRIMAL BLOCK-ANGULAR STRUCTURE

Info Detail Spesifik

https://doi.org/10.1287/ijoo.2019.0048

Pernyataan Tanggungjawab

Xin-Yee Lam, Defeng Sun, Kim-Chuan Toh

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