A Brief History of Linear and Mixed-Integer Programming Computation

By Robert E. Bixby. 2012

257 citations recorded by the source corpus.

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In Mathematical Optimization

Citations in the corpus

Measuring the Algorithmic Efficiency of Neural Networks (2020, background): “Progress on mixed integer programming was particularly straightforward to measure, so we’ve extended the original analysis of that domain below [Bixby, 2012].”
Mathematical optimization in classification and regression trees (2021, background): “In recent times, and because of the dramatic improvements in hardware and optimization solvers (Bixby 2012), many papers on building optimal (in some sense) classification and regression trees have appeared.”
Learning Optimal Classification Trees: Strong Max-Flow Formulations (2020, background): “Indeed, solvers such as CPLEX (2009) and Gurobi Optimization (2015) have beneﬁted from decades of research, see Bixby (2012), and have been very successful at solving a broad class of MIP problems.”
Optimal Generalized Decision Trees via Integer Programming (2016, methodology): “As such, we can utilize signiﬁcant advances in the power of modern MILP solvers [2, 1].”
The Discrete Dantzig Selector: Estimating Sparse Linear Models via Mixed Integer Linear Optimization (2015, background): “Consequently, estimator β̂ P satisfies the oracle property in the sense of Fan and Li [20].”
Matching for Balance (2019, methodology): “Matching for balance exemplifies how tools from modern optimization (e.g., Jünger et al. 2009 and Bixby 2012) can play a central role in the design of observational studies in general (e.g., Rosenbaum 2002 and Imbens and Rubin 2015) and in matching for aggregate covariate balance in particular…”
Optimal trees for prediction and prescription (2018, methodology): “To quantify this increase, Bixby [22] tested a set of MIO problems on the same computer using CPLEX 1.2, released in 1991, through CPLEX 11, released in 2007.”
Output Range Analysis for Deep Feedforward Neural Networks (2018, methodology): “The optimization problems are solved directly using an off-the-shelf MILP solver [28, 4].”