Abstract
We construct some classes of test problems of minimizing a concave or, more general, quasiconcave function over a polyhedral set. These test problems fulfil the general requirement that they have a global solution at a known point which is suitably chosen on the boundary of the feasible set.
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References
Floudas, C.A. and Pardalos, P.M. (1990),A Collection of Test Problems for Constrained Global Optimization Algorithms, Lecture Notes in Computer Science, 455, Springer-Verlag, Berlin.
Hager, W.W., Pardalos, P.M., Roussos, I.M. and Sahinoglou, H.D. (1991), Active Constraints, Indefinite Quadratic Programming, and Test Problems,Journal of Optimization Theory and Applications 68 (3), 499–511.
Horst, R. and Thoai, N.V. (1989), Modification, Implementation and Comparison of Three Algorithms for Globally Solving Linearly Constrained Concave Minimization Problems,Computing 42, 271–289.
Horst, R. and Tuy, H. (1993),Global Optimization: Deterministic Approaches, 2nd revised edition, Springer Verlag, Berlin.
Horst, R., Thoai, N.V. and Benson, H.P. (1991), Con Minimization via Conical Partitions and Polyhedral Outer Approximation,Mathematical Programming 50, 259–274.
Kalantari, B. and Rosen, J.B. (1986), Construction of Large-Scale Global Minimimum Concave Test Problems,Journal of Optimization Theory and Applications 48, 303–313.
Li, Y. and Pardalos, P.M. (1992), Generating quadratic assignment test problems with known optimal permutations,Computational Optimization and Applications 1, (2), 163–184.
Pardalos, P.M. (1987), Generation of Large-Scale Quadratic Programs for Use as Global Optimization Test Problems,ACM Transactions on Mathematical Software 13, 133–137.
Pardalos, P.M. (1991), Construction of Test Problems in Quadratic Bivalent Program,ACM Transactions on Mathematical Software,17, (1), 74–87.
Pardalos, P.M. and Rosen, J.B. (1987),Constrained Global Optimization: Algorithms and Applications, Lecture Notes in Computer Science, 268, Springer Verlag, Berlin.
Sung, Y.Y. and Rosen, J.B. (1982), Global Minimum Test Problem Construction,Mathematical Programming 24, 353–355.
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Thoai, N.V. On the construction of test problems for concave minimization algorithms. J Glob Optim 5, 399–402 (1994). https://doi.org/10.1007/BF01096688
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DOI: https://doi.org/10.1007/BF01096688