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Sherali, Hanif D.; Fraticelli, Barbara M. P.

doi:10.1023/a:1013819515732

Cited by 62 publications

(1 citation statement)

References 12 publications

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“…Instead of only using the initial linear constraints Ax ≤ b to define X in (1), we exploit a linear programming (LP) relaxation of (1) that is available in LP-based spatial branch and bound. This relaxation contains Ax ≤ b but also linear constraints that have been derived from, e.g., integrality restrictions of variables (e.g., MIR cuts [48] and Gomory cuts [26]), gradient cuts [32], RLT cuts [56], SDP cuts [57], or other valid underestimators for each g i with i ∈ M . Using a linear relaxation A x ≤ b with…”

Section: Refined Milp Relaxationmentioning

confidence: 99%

On generalized surrogate duality in mixed-integer nonlinear programming

et al. 2021

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The most important ingredient for solving mixed-integer nonlinear programs (MINLPs) to global $$\epsilon $$ ϵ -optimality with spatial branch and bound is a tight, computationally tractable relaxation. Due to both theoretical and practical considerations, relaxations of MINLPs are usually required to be convex. Nonetheless, current optimization solvers can often successfully handle a moderate presence of nonconvexities, which opens the door for the use of potentially tighter nonconvex relaxations. In this work, we exploit this fact and make use of a nonconvex relaxation obtained via aggregation of constraints: a surrogate relaxation. These relaxations were actively studied for linear integer programs in the 70s and 80s, but they have been scarcely considered since. We revisit these relaxations in an MINLP setting and show the computational benefits and challenges they can have. Additionally, we study a generalization of such relaxation that allows for multiple aggregations simultaneously and present the first algorithm that is capable of computing the best set of aggregations. We propose a multitude of computational enhancements for improving its practical performance and evaluate the algorithm’s ability to generate strong dual bounds through extensive computational experiments.

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Section: Refined Milp Relaxationmentioning

confidence: 99%

On generalized surrogate duality in mixed-integer nonlinear programming

et al. 2021

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Reformulation‐Linearization Technique for MIPs

Sherali

2011

Wiley Encyclopedia of Operations Research and Management Science

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The reformulation‐linearization technique (RLT) for mixed‐integer programs is an automatic model enhancement approach that generates a hierarchy of relaxations spanning the spectrum from the continuous linear programming (LP) relaxation to the convex hull of feasible solutions. This process is applicable to both 0‐1 as well as general discrete programs, and can be further augmented through the use of classes of semidefinite cuts. Often, the first‐level relaxation itself provides a sufficiently tight model reformulation that significantly improves problem solvability. The RLT procedure also offers a unifying framework for solving continuous nonconvex factorable optimization problems to global optimality.

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On Solving Polynomial, Factorable, and Black-Box Optimization Problems Using the RLT Methodology

Sherali¹,

Desai²

Essays and Surveys in Global Optimization

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Cited by 62 publications

References 12 publications

On generalized surrogate duality in mixed-integer nonlinear programming

On generalized surrogate duality in mixed-integer nonlinear programming

Reformulation‐Linearization Technique for MIPs

On Solving Polynomial, Factorable, and Black-Box Optimization Problems Using the RLT Methodology

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