OBA

Author: Nitish Shirish Keskar

OBA is a second-order method for convex L1-regularized optimization with active-set prediction. OBA belongs to the family of Orthant-Based methods (such as OWL) and uses a selective-corrective mechanism which brings about increased efficiency and robustness.

Features

The OBA package

• allows for solving general convex L1-regularized problems including Logistic Regression and LASSO.
• is written in pure-MATLAB with minimal dependencies and emphasizes simplicity and cross-platform compatibility.
• includes both Newton and quasi-Newton options for the proposed algorithm.

Usage Guide

The algorithm can be run using the syntax

x = OBA(funObj,lambda,[options]);

Here,

• funObj is an object with member functions for computing the function, gradient and Hessian-vector products at the iterates. Logistic Regression and LASSO classes are provided with the package. The file funTemplate.m can be used as a base for designing a custom function.
• lambda is the positive scalar for inducing sparsity in the solution.
• options is an optional argument for changing the default parameters used in OBA. For ease of use, the user can generate the default options struct using options=GenOptions() and change the parameters therein before passing it to OBA.

The parameters and their default values are

•  `options.optol`: termination tolerance
      (default: 1e-6)
  

•  `options.qn`: Quasi-Newton, 0 (Newton's Method), or 1 (quasi-Newton)
      (default: 0)
  

•  `options.mem_size`: quasi-Newton memory size
      (default: 20)
  

•  `options.maxiter`: max number of iterations
      (default: 1000)
  

•  `options.printlev`: print level, 0 (no printing) or 1
      (default: 1)
  

•  `options.CGtol`: CG termination tolerance (for Newton's Method)
      (default: 1e-1)
  

•  `options.maxCGiter`: max number of CG iterations (Newton's Method)
      (default: 1000).
  

For a detailed documentation of OBA and its associated functions, use help OBA.

Citation

If you use OBA for your research, please cite the paper

@article{OBA_Keskar2016,
author = {N. Keskar and J. Nocedal and F. Öztoprak and A. Wächter},
title = {A second-order method for convex -regularized optimization with active-set prediction},
journal = {Optimization Methods and Software},
volume = {0},
number = {0},
pages = {1-17},
year = {0},
doi = {10.1080/10556788.2016.1138222},
URL = {http://dx.doi.org/10.1080/10556788.2016.1138222},
eprint = {http://dx.doi.org/10.1080/10556788.2016.1138222}
}