Author: Alexandra M. Newman ( Colorado School of Mines, Golden, Colorado ) & Martin Weiss (European Commissio)

Abstract :  As advanced undergraduate and graduate students in optimization begin conducting research, they must base their work on articles found in academic journals. However, there is often a gap between the levels at which a journal article and a textbook are written. Bridging that gap are tutorials on fundamental, yet advanced, concepts such as (i) algorithmic details of linear and mixed-integer optimizers, (ii) formulations that render models more tractable, (iii) descriptions of the mathematical structure of linear and mixed-integer programs, and (iv) manuals of modeling languages that enable quick implementation of formulations and of linear and mixedinteger solvers. This survey paper provides references to papers and reports whose purpose is to give overviews of linear and mixed-integer optimization. We also include seminal texts and journal articles on fundamental topics, and furnish references on applications whose implementation may have implications for more general problems with similar mathematical structure. We propose to guide graduate students to identify references that aid in their understanding of advanced journal articles and that help them write their own research articles.