Header-Only C++ Mathematical Optimization Library for 'Armadillo'

'Ensmallen' is a templated C++ mathematical optimization library (by the 'MLPACK' team) that provides a simple set of abstractions for writing an objective function to optimize. Provided within are various standard and cutting-edge optimizers that include full-batch gradient descent techniques, small-batch techniques, gradient-free optimizers, and constrained optimization. The 'RcppEnsmallen' package includes the header files from the 'Ensmallen' library and pairs the appropriate header files from 'armadillo' through the 'RcppArmadillo' package. Therefore, users do not need to install 'Ensmallen' nor 'Armadillo' to use 'RcppEnsmallen'. Note that 'Ensmallen' is licensed under 3-Clause BSD, 'Armadillo' starting from 7.800.0 is licensed under Apache License 2, 'RcppArmadillo' (the 'Rcpp' bindings/bridge to 'Armadillo') is licensed under the GNU GPL version 2 or later. Thus, 'RcppEnsmallen' is also licensed under similar terms. Note that 'Ensmallen' requires a compiler that supports 'C++14' and 'Armadillo' 10.8.2 or later.

Linear Programming / Optimization

Can be used to solve Linear Programming / Linear Optimization problems by using the simplex algorithm.

Discrete and Global Optimization Routines

The R package 'adagio' will provide methods and algorithms for (discrete) optimization, e.g. knapsack and subset sum procedures, derivative-free Nelder-Mead and Hooke-Jeeves minimization, and some (evolutionary) global optimization functions.

Manly Mixture Modeling and Model-Based Clustering

The utility of this package includes finite mixture modeling and model-based clustering through Manly mixture models by Zhu and Melnykov (2016) . It also provides capabilities for forward and backward model selection procedures.

Adequacy of Probabilistic Models and General Purpose Optimization

The main application concerns to a new robust optimization package with two major contributions. The first contribution refers to the assessment of the adequacy of probabilistic models through a combination of several statistics, which measure the relative quality of statistical models for a given data set. The second one provides a general purpose optimization method based on meta-heuristics functions for maximizing or minimizing an arbitrary objective function.

Functions for Optimal Non-Bipartite Matching

Perform non-bipartite matching and matched randomization. A "bipartite" matching utilizes two separate groups, e.g. smokers being matched to nonsmokers or cases being matched to controls. A "non-bipartite" matching creates mates from one big group, e.g. 100 hospitals being randomized for a two-arm cluster randomized trial or 5000 children who have been exposed to various levels of secondhand smoke and are being paired to form a greater exposure vs. lesser exposure comparison. At the core of a non-bipartite matching is a N x N distance matrix for N potential mates. The distance between two units expresses a measure of similarity or quality as mates (the lower the better). The 'gendistance()' and 'distancematrix()' functions assist in creating this. The 'nonbimatch()' function creates the matching that minimizes the total sum of distances between mates; hence, it is referred to as an "optimal" matching. The 'assign.grp()' function aids in performing a matched randomization. Note bipartite matching can be performed using the prevent option in 'gendistance()'.

Random Orthonormal Matrix Generation and Optimization on the Stiefel Manifold

Simulation of random orthonormal matrices from linear and quadratic exponential family distributions on the Stiefel manifold. The most general type of distribution covered is the matrix-variate Bingham-von Mises-Fisher distribution. Most of the simulation methods are presented in Hoff(2009) "Simulation of the Matrix Bingham-von Mises-Fisher Distribution, With Applications to Multivariate and Relational Data" . The package also includes functions for optimization on the Stiefel manifold based on algorithms described in Wen and Yin (2013) "A feasible method for optimization with orthogonality constraints" .

Large, Sparse Optimal Matching with Refined Covariate Balance

Tools for large, sparse optimal matching of treated units and control units in observational studies. Provisions are made for refined covariate balance constraints, which include fine and near-fine balance as special cases. Matches are optimal in the sense that they are computed as solutions to network optimization problems rather than greedy algorithms. See Pimentel, et al.(2015) and Pimentel (2016), Obs. Studies 2(1):4-23. The rrelaxiv package, which provides an alternative solver for the underlying network flow problems, carries an academic license and is not available on CRAN, but may be downloaded from Github at < https://github.com/josherrickson/rrelaxiv/>.

'Rcpp' Integration for Numerical Computing Libraries

A collection of open source libraries for numerical computing (numerical integration, optimization, etc.) and their integration with 'Rcpp'.

'ECOS' Plugin for the 'R' Optimization Infrastructure

Enhances the 'R' Optimization Infrastructure ('ROI') package with the Embedded Conic Solver ('ECOS') for solving conic optimization problems.