directed rounding – Optimization Online

Safe bounds in linear and mixed-integer programming

Published: 2002/06/18

(Mixed) Integer Linear Programming, Linear Programming branch-and-cut, certificate of infeasibility, directed rounding, generalized gomory cut, interval arithmetic, linear programming, lower bounds, mixed-integer programming, mixed-integer rounding, rounding errors, safe cuts, safe presolve

Current mixed-integer linear programming solvers are based on linear programming routines that use floating point arithmetic. Occasionally, this leads to wrong solutions, even for problems where all coefficients and all solution components are small integers. It is shown how, using directed rounding and interval arithmetic, cheap pre- and postprocessing of the linear programs arising in … Read more

Symbolic-Algebraic Computations in a Modeling Language for Mathematical Programming

Published: 2000/09/11, Updated: 2000/09/12

David M. Gay

Modeling Languages and Systems automatic differentiation, binary-decimal conversion, directed rounding, presolve

AMPL is a language and environment for expressing and manipulating mathematical programming problems, i.e., minimizing or maximizing an algebraic objective function subject to algebraic constraints. AMPL permits separating a model, i.e., a symbolic representation of a class of problems, from the data required to specify a particular problem instance. Once AMPL has a problem instance, … Read more