5 research outputs found
CVXR: An R Package for Disciplined Convex Optimization
CVXR is an R package that provides an object-oriented modeling language for
convex optimization, similar to CVX, CVXPY, YALMIP, and Convex.jl. It allows
the user to formulate convex optimization problems in a natural mathematical
syntax rather than the restrictive form required by most solvers. The user
specifies an objective and set of constraints by combining constants,
variables, and parameters using a library of functions with known mathematical
properties. CVXR then applies signed disciplined convex programming (DCP) to
verify the problem's convexity. Once verified, the problem is converted into
standard conic form using graph implementations and passed to a cone solver
such as ECOS or SCS. We demonstrate CVXR's modeling framework with several
applications.Comment: 34 pages, 9 figure
Saturating Splines and Feature Selection.
We extend the adaptive regression spline model by incorporating saturation, the natural requirement that a function extend as a constant outside a certain range. We fit saturating splines to data via a convex optimization problem over a space of measures, which we solve using an efficient algorithm based on the conditional gradient method. Unlike many existing approaches, our algorithm solves the original infinite-dimensional (for splines of degree at least two) optimization problem without pre-specified knot locations. We then adapt our algorithm to fit generalized additive models with saturating splines as coordinate functions and show that the saturation requirement allows our model to simultaneously perform feature selection and nonlinear function fitting. Finally, we briefly sketch how the method can be extended to higher order splines and to different requirements on the extension outside the data range