1,293 research outputs found
Projection methods in conic optimization
There exist efficient algorithms to project a point onto the intersection of
a convex cone and an affine subspace. Those conic projections are in turn the
work-horse of a range of algorithms in conic optimization, having a variety of
applications in science, finance and engineering. This chapter reviews some of
these algorithms, emphasizing the so-called regularization algorithms for
linear conic optimization, and applications in polynomial optimization. This is
a presentation of the material of several recent research articles; we aim here
at clarifying the ideas, presenting them in a general framework, and pointing
out important techniques
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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