153 research outputs found
COIN/BCP user’s manual
No full textcfl2001 International Business Machines Corporation, Ted Ralphs and others. All righ
Contents
No full textc○2001 International Business Machines Corporation, Ted Ralphs and others. All righ
A unified framework for multistage mixed integer linear optimization
No full textWe introduce a unified framework for the study of multilevel mixed integer linear optimization problems and multistage stochastic mixed integer linear optimization problems with recourse. The framework highlights the common mathematical structure of the two problems and allows for the development of a common algorithmic framework. Focusing on the two-stage case, we investigate, in particular, the nature of the value function of the second-stage problem, highlighting its connection to dual functions and the theory of duality for mixed integer linear optimization problems, and summarize different reformulations. We then present two main solution techniques, one based on a Benders-like decomposition to approximate either the risk function or the value function, and the other one based on cutting plane generation.</p
Bilevel Programming and Maximally Violated Valid Inequalities
No full textIn recent years, branch-and-cut algorithms have become firmly established as the most effective method for solving generic mixed integer linear programs (MIPs). Methods for automatically generating inequalities valid for the convex hull of solutions to such MIPs are a critical element of branch-and-cut. This paper examines the nature of the so-called separation problem, which is that of generating a valid inequality violated by a given real vector, usually arising as the solution to a relaxation of the original problem. We show that the prob- lem of generating a maximally violated valid inequality often has a natural interpretation as a bilevel program. In some cases, this bilevel program can be easily reformulated as a single-level mathematical program, yielding a stan- dard mathematical programming formulation for the separation problem. In other cases, no reformulation exists. We illustrate the principle by considering the separation problem for two well-known classes of valid inequalities
A Conic Representation of the Convex Hull of Disjunctive Sets and Conic Cuts for Integer Second Order Cone Optimization
No full text
A complete characterization of disjunctive conic cuts for mixed integer second order cone optimization
No full textBilevel programming and the separation problem
No full textIn recent years, branch-and-cut algorithms have become firmly established as the most effective method for solving generic mixed integer linear programs (MILPs). Methods for automatically generating inequalities valid for the convex hull of solutions to such MILPs are a critical element of branch-and-cut. This paper examines the nature of the so-called separation problem, which is that of generating a valid inequality violated by a given real vector, usually arising as the solution to a relaxation of the original problem. We show that the problem of generating a maximally violated valid inequality often has a natural interpretation as a bilevel program. In some cases, this bilevel program can be easily reformulated as a simple single-level mathematical program, yielding a standard mathematical programming formulation for the separation problem. In other cases, no such polynomial-size single-level reformulation exists unless the polynomial hierarchy collapses to its first level (an event considered extremely unlikely in computational complexity theory). We illustrate our insights by considering the separation problem for two well-known classes of valid inequalities. Keywords: Bilevel programming; Cutting planes; Separation; Computational complexit
coin-or/COIN-OR-OptimizationSuite: Version 1.8.0
No full textA harness for building the bundled suite of all the optimization tools available in the COIN-OR repository. This repository is mirrored from https://projects.coin-or.org/CoinBinar
INFORMSJoC/2020.0340: Archived version of code for IJOC Manuscript 2020.0340
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