Abstract
Construction of problems with known global solutions is important for the computational testing of constrained global minimization algorithms. In this paper, it is shown how to construct a concave quadratic function which attains its global minimum at a specified vertex of a polytope inR n+k. The constructed function is strictly concave in the variablesx ∈R n and is linear in the variablesy ∈R k. The number of linear variablesk may be much larger thann, so that large-scale global minimization test problems can be constructed by the methods described here.
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Communicated by O. L. Mangasarian
This research was supported by the Computer Science Section of the National Science Foundation under Grant No. MCS-81-01214.
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Kalantari, B., Rosen, J.B. Construction of large-scale global minimum concave quadratic test problems. J Optim Theory Appl 48, 303–313 (1986). https://doi.org/10.1007/BF00940675
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DOI: https://doi.org/10.1007/BF00940675