Optimization over integers

By Dimitris J. Bertsimas, R. Weismantel. 2005

396 citations recorded by the source corpus.

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Citations in the corpus

Best Subset Selection via a Modern Optimization Lens (2015, methodology): “gative reals, the symbol denotes element-wise inequalities and we optimize over m2R containing both discrete ( i;i2I) and continuous ( i;i=2I) variables, with Iˆf1;:::;mg. For background on MIO see [4]. Subclasses of MIQO problems include convex quadratic optimization problems (I= ;), mixed integer”
Nonlinear Discrete Optimization (2010, background): “More recent sources on integer programming containing also material on nonlinear optimization and on mixed integer programming, where some of the variables are integer and some are real, are the book [14] by Bertsimas and Weismantel and survey [49] by Hemmecke, Köppe, Lee, and Weismantel.”
Near optimal placement of virtual network functions (2015, background): “The NFV location problem captures two well known NPhard optimization problems problems - the facility location problem and the generalized assignment problem (GAP), both of which received much attention in the last 50 years [10], [2].”
Optimal classification trees (2017, background): “Injecting a strong warm start solution before starting the solver greatly increases the speed with which the solver is able to generate strong feasible solutions (Bertsimas and Weismantel 2005).”
Mixed Integer Linear Programming Formulation Techniques (2015, methodology): “For more details on basic branch-and-bound and state-of-the-art solvers, we refer the reader to [22, 36, 131, 166] and [1, 2, 25, 23, 92, 112, 24], respectively.”
Optimal trees for prediction and prescription (2018, background): “Injecting a strong warm start solution before starting the solver greatly increases the speed with which the solver is able to generate strong feasible solutions [17].”
How to reverse-engineer quality rankings (2012, background): “In fact, the ability to solve an MIO problem depends critically on the choice of formulation (see Bertsimas and Weismantel 2005, for details).”
The Discrete Dantzig Selector: Estimating Sparse Linear Models via Mixed Integer Linear Optimization (2015, methodology): “where, MU is a large but finite number [23].”
Integer optimization methods for machine learning (2012, background): “An MIO formulation is stronger if its linear relaxation corresponds to a smaller feasible set; in particular, it is stronger if it is closer to the convex hull of F [see Bertsimas and Weismantel, 2005, for details].”
Integer and Combinatorial Optimization (2013, background): “Texts covering the theory of linear and integer linear optimization include those of Bertsimas and Weismantel (2005), Chvátal (1983), Nemhauser and Wolsey (1988), Parker and Rardin (1988), Schrijver (1986), and Wolsey (1998). Overviews of combinatorial optimization are provided by Papadimitriou and ”
Least quantile regression via modern optimization (2013, methodology): “The constraint µ i µ i = 0 can be modeled via integer optimization using Specially Ordered Sets of Type 1 (Bertsimas and Weismantel, 2005), i.e., SOS-1 constraints as follows: for every i = 1 , . . . , n.”
Journal of the American Statistical Association Using Mixed Integer Programming for Matching in an Observational Study of Kidney Failure after Surgery Using Mixed Integer Programming for Matching in an Observational Study of Kidney Failure after Surgery (unknown): “However , in recent years, there have been important advances in linear programming (LP), which is the facilitating technology for solving MIPs (Bixby et al. 2000; Bertsimas and Weismantel 2005).”