51 research outputs found
SDPNAL+: A Matlab software for semidefinite programming with bound constraints (version 1.0)
SDPNAL+ is a {\sc Matlab} software package that implements an augmented
Lagrangian based method to solve large scale semidefinite programming problems
with bound constraints. The implementation was initially based on a majorized
semismooth Newton-CG augmented Lagrangian method, here we designed it within an
inexact symmetric Gauss-Seidel based semi-proximal ADMM/ALM (alternating
direction method of multipliers/augmented Lagrangian method) framework for the
purpose of deriving simpler stopping conditions and closing the gap between the
practical implementation of the algorithm and the theoretical algorithm. The
basic code is written in {\sc Matlab}, but some subroutines in C language are
incorporated via Mex files. We also design a convenient interface for users to
input their SDP models into the solver. Numerous problems arising from
combinatorial optimization and binary integer quadratic programming problems
have been tested to evaluate the performance of the solver. Extensive numerical
experiments conducted in [Yang, Sun, and Toh, Mathematical Programming
Computation, 7 (2015), pp. 331--366] show that the proposed method is quite
efficient and robust, in that it is able to solve 98.9\% of the 745 test
instances of SDP problems arising from various applications to the accuracy of
in the relative KKT residual
Fast algorithms for large scale generalized distance weighted discrimination
High dimension low sample size statistical analysis is important in a wide
range of applications. In such situations, the highly appealing discrimination
method, support vector machine, can be improved to alleviate data piling at the
margin. This leads naturally to the development of distance weighted
discrimination (DWD), which can be modeled as a second-order cone programming
problem and solved by interior-point methods when the scale (in sample size and
feature dimension) of the data is moderate. Here, we design a scalable and
robust algorithm for solving large scale generalized DWD problems. Numerical
experiments on real data sets from the UCI repository demonstrate that our
algorithm is highly efficient in solving large scale problems, and sometimes
even more efficient than the highly optimized LIBLINEAR and LIBSVM for solving
the corresponding SVM problems
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