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Abstract:

It is known that point searching in basic semialgebraic sets and the search for globally minimal points in polynomial optimization tasks can be carried out using (sd) O(n) arithmetic operations, where n and s are the numbers of variables and constraints and d is the maximal degree of the polynomials involved. Subject to certain conditions, we associate to each of these problems an intrinsic system degree which becomes in worst case of order (nd) O(n) and which measures the intrinsic complexity of the task under consideration. We design non-uniform deterministic or uniform probabilistic algorithms of intrinsic, quasi-polynomial complexity which solve these problems. © 2014 Elsevier Inc. All rights reserved.

Registro:

Documento: Artículo
Título:Intrinsic complexity estimates in polynomial optimization
Autor:Bank, B.; Giusti, M.; Heintz, J.; Safey El Din, M.
Filiación:Humboldt-Universität zu Berlin, Institut für Mathematik, 10099 Berlin, Germany
CNRS, Lab. LIX, École Polytechnique, 91228 Palaiseau Cedex, France
Departamento de Computación, Universidad de Buenos Aires, Ciudad University, 1428 Buenos Aires, Argentina
Departamento de Matemáticas, Estadística y Computación, Universidad de Cantabria, 39071 Santander, Spain
Sorbonne Universities, Univ. Pierre et Marie Curie (Paris 06), Institut Universitaire de France, France
Palabras clave:Degree of varieties; Intrinsic complexity; Polynomial optimization; Computational complexity; Numerical analysis; Arithmetic operations; Complexity estimates; Degree of varieties; Intrinsic complexity; Polynomial optimization; Probabilistic algorithm; Quasi-poly-nomial; Semi-algebraic sets; Polynomials
Año:2014
Volumen:30
Número:4
Página de inicio:430
Página de fin:443
DOI: http://dx.doi.org/10.1016/j.jco.2014.02.005
Título revista:Journal of Complexity
Título revista abreviado:J. Complexity
ISSN:0885064X
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0885064X_v30_n4_p430_Bank

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Citas:

---------- APA ----------
Bank, B., Giusti, M., Heintz, J. & Safey El Din, M. (2014) . Intrinsic complexity estimates in polynomial optimization. Journal of Complexity, 30(4), 430-443.
http://dx.doi.org/10.1016/j.jco.2014.02.005
---------- CHICAGO ----------
Bank, B., Giusti, M., Heintz, J., Safey El Din, M. "Intrinsic complexity estimates in polynomial optimization" . Journal of Complexity 30, no. 4 (2014) : 430-443.
http://dx.doi.org/10.1016/j.jco.2014.02.005
---------- MLA ----------
Bank, B., Giusti, M., Heintz, J., Safey El Din, M. "Intrinsic complexity estimates in polynomial optimization" . Journal of Complexity, vol. 30, no. 4, 2014, pp. 430-443.
http://dx.doi.org/10.1016/j.jco.2014.02.005
---------- VANCOUVER ----------
Bank, B., Giusti, M., Heintz, J., Safey El Din, M. Intrinsic complexity estimates in polynomial optimization. J. Complexity. 2014;30(4):430-443.
http://dx.doi.org/10.1016/j.jco.2014.02.005