Computation of Optimal Transport Plans and Wasserstein Distances

Solve optimal transport problems. Compute Wasserstein distances (a.k.a. Kantorovitch, Fortet--Mourier, Mallows, Earth Mover's, or minimal L_p distances), return the corresponding transference plans, and display them graphically. Objects that can be compared include grey-scale images, (weighted) point patterns, and mass vectors.

Limited-memory BFGS Optimization

A wrapper built around the libLBFGS optimization library by Naoaki Okazaki. The lbfgs package implements both the Limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) and the Orthant-Wise Quasi-Newton Limited-Memory (OWL-QN) optimization algorithms. The L-BFGS algorithm solves the problem of minimizing an objective, given its gradient, by iteratively computing approximations of the inverse Hessian matrix. The OWL-QN algorithm finds the optimum of an objective plus the L1-norm of the problem's parameters. The package offers a fast and memory-efficient implementation of these optimization routines, which is particularly suited for high-dimensional problems.

Solve Nonlinear Optimization with Nonlinear Constraints

Optimization for nonlinear objective and constraint functions. Linear or nonlinear equality and inequality constraints are allowed. It accepts the input parameters as a constrained matrix.

Optimal, Fast, and Reproducible Univariate Clustering

Fast, optimal, and reproducible weighted univariate clustering by dynamic programming. Four problems are solved, including univariate k-means (Wang & Song 2011) (Song & Zhong 2020) , k-median, k-segments, and multi-channel weighted k-means. Dynamic programming is used to minimize the sum of (weighted) within-cluster distances using respective metrics. Its advantage over heuristic clustering in efficiency and accuracy is pronounced when there are many clusters. Multi-channel weighted k-means groups multiple univariate signals into k clusters. An auxiliary function generates histograms adaptive to patterns in data. This package provides a powerful set of tools for univariate data analysis with guaranteed optimality, efficiency, and reproducibility, useful for peak calling on temporal, spatial, and spectral data.

A Replacement and Extension of the 'optim' Function

Provides a test of replacement and extension of the optim() function to unify and streamline optimization capabilities in R for smooth, possibly box constrained functions of several or many parameters. This version has a reduced set of methods and is intended to be on CRAN.

Multiple Criteria Optimization Algorithms and Related Functions

A collection of function to solve multiple criteria optimization problems using genetic algorithms (NSGA-II). Also included is a collection of test functions.

Bayesian Optimization and Model-Based Optimization of Expensive Black-Box Functions

Flexible and comprehensive R toolbox for model-based optimization ('MBO'), also known as Bayesian optimization. It implements the Efficient Global Optimization Algorithm and is designed for both single- and multi- objective optimization with mixed continuous, categorical and conditional parameters. The machine learning toolbox 'mlr' provide dozens of regression learners to model the performance of the target algorithm with respect to the parameter settings. It provides many different infill criteria to guide the search process. Additional features include multi-point batch proposal, parallel execution as well as visualization and sophisticated logging mechanisms, which is especially useful for teaching and understanding of algorithm behavior. 'mlrMBO' is implemented in a modular fashion, such that single components can be easily replaced or adapted by the user for specific use cases.

Genetic Algorithms

Flexible general-purpose toolbox implementing genetic algorithms (GAs) for stochastic optimisation. Binary, real-valued, and permutation representations are available to optimize a fitness function, i.e. a function provided by users depending on their objective function. Several genetic operators are available and can be combined to explore the best settings for the current task. Furthermore, users can define new genetic operators and easily evaluate their performances. Local search using general-purpose optimisation algorithms can be applied stochastically to exploit interesting regions. GAs can be run sequentially or in parallel, using an explicit master-slave parallelisation or a coarse-grain islands approach. For more details see Scrucca (2013) and Scrucca (2017) .

Limited Memory BFGS Minimizer with Bounds on Parameters with optim() 'C' Interface

Interfacing to Nocedal et al. L-BFGS-B.3.0 (See < http://users.iems.northwestern.edu/~nocedal/lbfgsb.html>) limited memory BFGS minimizer with bounds on parameters. This is a fork of 'lbfgsb3'. This registers a 'R' compatible 'C' interface to L-BFGS-B.3.0 that uses the same function types and optimization as the optim() function (see writing 'R' extensions and source for details). This package also adds more stopping criteria as well as allowing the adjustment of more tolerances.

Approximate Optimal Transport Between Two-Dimensional Grids

Can be used for optimal transport between two-dimensional grids with respect to separable cost functions of l^p form. It utilizes the Frank-Wolfe algorithm to approximate so-called pivot measures: one-dimensional transport plans that fully describe the full transport, see G. Auricchio (2021) . For these, it offers methods for visualization and to extract the corresponding transport plans and costs. Additionally, related functions for one-dimensional optimal transport are available.