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Numerical optimization is often an essential aspect of mathematical analysis in science, technology and other areas. The function optim() provides basic optimization capabilities and is among the most widely used functions in R . Additionally, there are various packages and functions for solving various types of optimization problem (the optimization task view on Comprehensive R Archive Network provides a comprehensive list of available options for solving optimization problems in R). In this special volume, four papers are presented which discuss some of the areas in numerical optimization where significant developments have been made recently to enhance the capabilities in R . This introduction provides a brief overview of the volume.