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This chapter describes the reformulation–linearization technique (RLT) for solving mixed-integer 0-1 and general mixed-discrete optimization problems. The use of RLT for directly lifting mixed-integer programs (MIPs) into higher-dimensional representations as well as for deriving strong valid inequalities in the space of the original variables is discussed. Methods for exploiting inherent special structures for particular applications as well as for enhancing RLT-based relaxations in general through conditional logic deductions and semidefinite cuts are also presented. Finally, certain persistency results and extensions to solving general mixed-discrete convex programs, as well as continuous, nonconvex factorable programming problems, along with implementation guidelines are outlined.

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Reformulation–Linearization Techniques for Mixed-Discrete Optimization Problems

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  • 发表日期：

    2025年

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  • Hanif D. Sherali,
  • Warren P. Adams

摘要

This chapter describes the reformulation–linearization technique (RLT) for solving mixed-integer 0-1 and general mixed-discrete optimization problems. The use of RLT for directly lifting mixed-integer programs (MIPs) into higher-dimensional representations as well as for deriving strong valid inequalities in the space of the original variables is discussed. Methods for exploiting inherent special structures for particular applications as well as for enhancing RLT-based relaxations in general through conditional logic deductions and semidefinite cuts are also presented. Finally, certain persistency results and extensions to solving general mixed-discrete convex programs, as well as continuous, nonconvex factorable programming problems, along with implementation guidelines are outlined.