Une borne optimale pour la programmation entière quasi-convexe

Bernd Bank; Joos Heintz; Teresa Krick; Reinhard Mandel; Pablo Solernó

Bulletin de la Société Mathématique de France (1993)

  • Volume: 121, Issue: 2, page 299-314
  • ISSN: 0037-9484

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Bank, Bernd, et al. "Une borne optimale pour la programmation entière quasi-convexe." Bulletin de la Société Mathématique de France 121.2 (1993): 299-314. <http://eudml.org/doc/87668>.

@article{Bank1993,
author = {Bank, Bernd, Heintz, Joos, Krick, Teresa, Mandel, Reinhard, Solernó, Pablo},
journal = {Bulletin de la Société Mathématique de France},
keywords = {quasiconvex polynomials; system of polynomial inequalities; geometrical bound},
language = {fre},
number = {2},
pages = {299-314},
publisher = {Société mathématique de France},
title = {Une borne optimale pour la programmation entière quasi-convexe},
url = {http://eudml.org/doc/87668},
volume = {121},
year = {1993},
}

TY - JOUR
AU - Bank, Bernd
AU - Heintz, Joos
AU - Krick, Teresa
AU - Mandel, Reinhard
AU - Solernó, Pablo
TI - Une borne optimale pour la programmation entière quasi-convexe
JO - Bulletin de la Société Mathématique de France
PY - 1993
PB - Société mathématique de France
VL - 121
IS - 2
SP - 299
EP - 314
LA - fre
KW - quasiconvex polynomials; system of polynomial inequalities; geometrical bound
UR - http://eudml.org/doc/87668
ER -

References

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  1. [1] BANK (B.) and MANDEL (R.). — Parametric integer optimization. - Akademie-Verlag, Berlin, 1988. Zbl0643.90043MR89m:90119
  2. [2] BANK (B.) and MANDEL (R.). — (Mixed-)Integer solutions of quasiconvex polynomial inequalities, Math. Res., t. 45, 1988, p. 20-34. Zbl0657.90071MR89i:90088
  3. [3] HEINTZ (J.), ROY (M.-F.) and SOLERNÓ (P.). — On the complexity of semialgebraic sets (Extended abstract), Proc. IFIP Congress'89, IX World Computer Congress, North-Holland, 1989, p. 293-298. 
  4. [4] HEINTZ (J.), ROY (M.-F.) et SOLERNÓ (P.). — Complexité du principe de Tarski-Seidenberg, C. R. Acad. Sci. Paris Sér. I Math., t. 309, 1989, p. 825-830. Zbl0704.03013MR92c:12012
  5. [5] HEINTZ (J.), ROY (M.-F.) et SOLERNÓ (P.). — Sur la complexité du principe de Tarski-Seidenberg, Bull. Soc. Math. France, t. 118, 1990, p. 101-126. Zbl0767.03017MR92g:03047
  6. [6] KHACHIYAN (L.G.). — Convexity and complexity in polynomial programming. - Proc. Int. Congress Math., Varsovie, 1983, p. 1569-1577. Zbl0588.90070MR87a:90097
  7. [7] KRICK (T.). — Complejidad para problems de geometría elemental, Thèse, Université de Buenos Aires, 1990. 
  8. [8] MIGNOTTE (M.). — Mathématiques pour le calcul formel. - P.U.F, 1989. Zbl0679.12001MR91a:68001
  9. [9] RENEGAR (J.). — On the computational complexity and geometry of the first order theory of the reals, Part III, Quantifier elimination, I. Symbolic Computation, t. 13, 1992, p. 329-352. Zbl0798.68073MR93h:03011c
  10. [10] ROCKAFELLAR (R.T.). — Convex Analysis. - Princeton Mathematical Series 28, 1970. Zbl0193.18401MR43 #445
  11. [11] SCHRIJVER (A.). — Theory of linear and integer programming. - Wiley Interscience Series in Discrete Mathematics, 1989. 
  12. [12] SOLERNÓ (P.). — Complejidad de conjuntos semialgebraicos, Thèse, Université de Buenos Aires, 1989. 
  13. [13] TARASOV (S.P.) and KHACHIYAN (L.G.). — Bounds of solutions and algorithmic complexity of systems of convex diophantine inequalities, Soviet. Math. Dokl., t. 22, 3, 1980, p. 700-704. Zbl0467.90048

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