Direct descent methods for minimizing objective functions of support vector regression type
M. R. Osborne and G. A. Watson
Abstract:
The problem of minimizing the sum of a smooth (convex)
function plus a piecewise linear separable (convex) function is
called a problem of support vector regression type. Such problems
prove to have many applications in Statistics and Data Mining, for
example. It is typically the case that they can be formulated as
smooth, linearly constrained optimization problems. However, this
can require the introduction of many additional variables. For
this reason we consider the development of compact descent
algorithms, essentially analogous to active set methods, which
exploit the special structure of the support vector regression
function. Numerical results are presented for a selection of
problems to illustrate the effectiveness of our approach. These
show that, as in the purely polyhedral case, attention to the form
of the line search can pay dividends.
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