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Convexity and concavity detection in computational graphs: tree walks for convexity assessment. (English) Zbl 1243.90004

Summary: 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 [H. Schichl, “COCONUT: COntinuous CONstraints –Updating the Technology”, http://www.mat.univie.ac.at/users/neum/public_html/glopt/coconut/] focusses on nonlinear global continuous optimization and possesses its own modeling language and data structures. The Dr. AMPL meta-solver [R. Fourer and D. Orban [Comput. Manag. Sci. 7, No. 4, 437-463 (2010; Zbl 1243.90005)] aims to analyze nonlinear differentiable optimization models and hooks into the AMPL Solver Library [D. M. Gay, “Hooking your solver to AMPL”, Tech. Rep. 97-4-06, Bell Labs, Murray Hill, NJ, http://www.ampl.com/REFS/hooking2.pdf]. 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.

MSC:

90-04 Software, source code, etc. for problems pertaining to operations research and mathematical programming
90C30 Nonlinear programming
90C35 Programming involving graphs or networks
68W30 Symbolic computation and algebraic computation

Citations:

Zbl 1243.90005
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