Convexity and concavity detection in computational graphs: Tree walks for convexity assessment

Convexity and concavity detection in computational graphs: Tree walks for convexity assessment

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Article ID: iaor20101959
Volume: 22
Issue: 1
Start Page Number: 26
End Page Number: 43
Publication Date: Dec 2010
Journal: INFORMS Journal on Computing
Authors: , , , ,
Abstract:

We examine symbolic tools associated with two modeling systems for mathematical programming, which can be used to automatically detect the presence or absence of convexity and concavity in the objective and constraint functions, as well as convexity of the feasible set in some cases. The coconut solver system [2004] focuses on nonlinear global continuous optimization and possesses its own modeling language and data structures. The Dr. Ampl meta-solver [2007] aims to analyze nonlinear differentiable optimization models and hooks into the ampl Solver Library [2002]. Our symbolic convexity analysis may be supplemented, when it returns inconclusive results, with a numerical phase that may detect nonconvexity. We report numerical results using these tools on sets of test problems for both global and local optimization.

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