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Global optimization using interval arithmetic. (English) Zbl 0797.90113

Summary: Interval arithmetic provides an efficient method of global optimization. With less efficiency all stationary points of a function can be found. A minimization method is described and applied to an econometric function. The results are compared with the method of simulated annealing on the same function.

MSC:

90C90 Applications of mathematical programming
62P20 Applications of statistics to economics
65G30 Interval and finite arithmetic
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References:

[1] Gay, David. M., 1988, Interval least squares?a diagnostic tool,Reliability in Computing-The Role of Interval Methods in Scientific Computing, R. E. Moore, (ed.), Academic Press, Boston.
[2] Goffe, William L., Gary D. Ferrier, and John Rodgers, 1992, Simulated annealing: An initial application in econometrics,Computer Science in Economics and Management 5 133-146 · Zbl 0850.62871 · doi:10.1007/BF00436486
[3] Gross, Beate, 1993, Verification of asymptotic stability for inverse matrices and applications in control theory,Scientific Computing with Automatic Result Verification, Mathematics in Science and Engineering, Vol. 189, E. Adams and U. Kulisch (eds.), Academic Press, Boston, pp. 357-396. · Zbl 0796.65084
[4] Hansen, Eldon, 1992,Global Optimization Using Interval Analysis, Marcel Dekker, New York. · Zbl 0762.90069
[5] Jansson, Christian, 1988, A self-validating method for solving linear programming problems with interval input data,Scientific Computation with Automatic Result Verification, Computing Supplementum 6, U. Kulish and H.J. Stetter (eds.), springer-Verlag, New York, pp. 33-46. · Zbl 0661.65056
[6] Judge, George. G., R. Carter Hill, W. E. Griffiths, Helmut Lütkepohl, and Tsoung-Chao Lee 1982,Introduction to the Theory and Practice of Econometrics, John Wiley & Sons, New York.
[7] Kearfott, R. B., and M. Novoa III., 1990, Algorithm 681: INTBIS, a portable interval Newton/bisection package,ACM Transactions on Mathematical Software,16, 152-157. · Zbl 0900.65152 · doi:10.1145/78928.78931
[8] Klatte, R., U. Kulish, A. Wiethoff, C. Lawo and M. Rauch, 1993,C-XSC AC++ Library for Extended Scientific Computing, Springer-Verlag, Berlin.
[9] Klatte, R., U. Kulisch, M. Neaga, D. Ratz and C. Ullrich, 1992PASCAL-XSC Language Reference with Examples, Springer, Heidelberg. · Zbl 0875.68228
[10] Moore, Ramon E., 1959, Automatic error analysis in digital computation, Technical Report LMSD-4842, Lockheed Missiles and Space Division, Sunnyvale, California.
[11] Moore, R. E., 1979,Methods and Applications of Interval Analysis, SIAM Press, Philadelphia. · Zbl 0417.65022
[12] Neumaier, Arnold., 1990,Interval Methods for Systems of Equations, Cambridge University Press, Cambridge. · Zbl 0715.65030
[13] Ratschek, H. and J. Rokne, 1988,New Computer Methods for Global Optimization, Ellis Horwood Limited, Chichester. · Zbl 0648.65049
[14] Törn, Aimo and Antanas ?ilinskas, 1989,Global Optimization, Lecture Notes in Computer Science Vol. 350, Springer-Verlag, Berlin.
[15] Walter, Wolfgang V., 1993, ACRITH-XSC, A fortran-like language for verified scientific computing,Scientific Computing with Automatic Result Verification, Mathematics in Science and Engineering, Vol. 189, E. Adams and U. Kulisch, (eds.) Academic Press, Boston, pp. 45-70. · Zbl 0801.68019
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