Decomposition approach for the global minimization of biconcave functions over polytopes
- 64 Downloads
A decomposition approach is proposed for minimizing biconcave functions over polytopes. Important special cases include concave minimization, bilinear and indefinite quadratic programming for which new algorithms result. The approach introduces a new polyhedral partition and combines branch-and-bound techniques, outer approximation, and projection of polytopes in a suitable way.
Key WordsGlobal optimization biconcave programming concave minimization bilinear and quadratic programming branch-and-bound algorithms outer approximations.
Unable to display preview. Download preview PDF.
- 1.Al-Khayyal, F. A.,Constrained Bilinear Programming and Jointly Related Problems, Report J-83-3, Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia, 1983.Google Scholar
- 2.Horst, R., andTuy, H.,On the Convergence of Global Methods in Multiextremal Optimization, Journal of Optimization Theory and Applications, Vol. 54, pp. 253–271, 1987.Google Scholar
- 3.Horst, R., andTuy, H.,Global Optimization: Deterministic Approaches 2nd Revised Edition, Springer, Berlin, Germany, 1993.Google Scholar
- 4.Thoai, N. V., andTuy, H.,Convergent Algorithms for Minimizing a Concave Function, Mathematics of Operations Research, Vol. 5, pp. 556–566, 1980.Google Scholar
- 5.Horst, R., andTuy, H.,Convergence and Restart in Branch-and-Bound Algorithms for Global Optimization: Application to Concave Minimization and DC-Optimization Problems, Mathematical Programming, Vol. 41, pp. 161–183, 1988.Google Scholar
- 6.Horst, R.,An Algorithm for Nonconvex Programming Problems, Mathematical Programming, Vol. 10, pp. 312–321, 1976.Google Scholar
- 7.Benson, H. P.,Concave Minimization, Handbook of Global Optimization, Edited by R. Horst and P. Pardalos, Kluwer Academic Publishers, Dordrecht, Netherlands, pp. 43–148, 1995.Google Scholar
- 8.Horst, R., Thoai, N. V., andDe Vries, J.,On Finding New Vertices and Redundant Constraints in Cutting-Plane Algorithms for Global Optimization, Operations Research Letters, Vol. 7, pp. 85–90, 1988.Google Scholar
- 9.Chen, P. C., Hansen, P., andJaumard, B.,On-Line and Off-Line Vertex Enumeration by Adjacency Lists, Operations Research Letters, Vol. 10, pp. 403–409, 1991.Google Scholar
- 10.Tuy, H.,Concave Minimization under Linear Constraints with Special Structure, Optimization, Vol. 16, pp. 335–352, 1985.Google Scholar
- 11.Horst, R., andThoai, N. V.,Constraints Decomposition Algorithms in Global Optimization, Journal of Global Optimization, Vol. 5, pp. 333–348, 1994.Google Scholar
- 12.Thoai, N. V.,A Global Optimization Approach for Solving Convex Multiplicative Programming Problems, Journal of Global Optimization, Vol. 1, pp. 341–357, 1991.Google Scholar
- 13.Thoai, N. V.,Canonical DC-Programming Techniques for Solving a Convex Program with an Additional Constraint of Multiplicative Type, Computing, Vol. 50, pp. 241–253, 1993.Google Scholar
- 14.Horst, R., andThoai, N. V.,A New Algorithm for Solving the General Quadratic Problem, Computational Optimization and Applications Vol. 5, pp. 39–48, 1990.Google Scholar
- 15.Horst, R., andThoai, N. V.,Modification Implementation and Comparison of Three Algorithms for Globally Solving Linearly-Constrained Concave Minimization Problems, Computing, Vol. 42, pp. 271–289, 1989.Google Scholar
- 16.Horst, R., Thoai, N. V., andBenson, H. P.,Concave Minimization via Conical Partitions and Polyhedral Outer Approximation, Mathematical Programming, Vol. 50, pp. 259–274, 1991.Google Scholar