Quasi-convexity, strictly quasi-convexity and pseudo-convexity of composite objective functions
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 6 (1972) no. R1, pp. 15-26.
@article{M2AN_1972__6_1_15_0,
author = {Bereanu, Bernard},
title = {Quasi-convexity, strictly quasi-convexity and pseudo-convexity of composite objective functions},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
pages = {15--26},
publisher = {Dunod},
volume = {6},
number = {R1},
year = {1972},
zbl = {0268.90052},
mrnumber = {318417},
language = {en},
url = {http://archive.numdam.org/item/M2AN_1972__6_1_15_0/}
}
Bereanu, Bernard. Quasi-convexity, strictly quasi-convexity and pseudo-convexity of composite objective functions. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 6 (1972) no. R1, pp. 15-26. http://archive.numdam.org/item/M2AN_1972__6_1_15_0/

[1] K. J. Arrow and A. C. Enthoven, « Quasi-coneave programming », Econo-metrica, 29 (1961), 779-800. | MR 138509 | Zbl 0104.14302

[2] J. L. Bauntfy, Nonlinear programming for models with joint constraints, in Abadie J. (ed) Integer and nonlinear programming, North-Holland (1970), 337-352. | Zbl 0334.90054

[3] B. Bereanu, « Programme de risque minimal en programmation linéaire sto-chastique », C.R. Acad. Sci. Paris, 258 (1964), 5, 981-983. | MR 167333 | Zbl 0123.37301

[4] B. Bereanu, « On the composition of convex functions », Rev. Roum. Math.Pures AppL, 14 (1969), 1078-1084, | MR 252586 | Zbl 0191.06204

[5] C. R. Bector, « Indefinite quadratic programming with Standard errors in objective », Cahiers Centre d'Étude Recherche Opér. 10 (1968), 4, 247-253. | MR 247876 | Zbl 0169.22202

[6] C. Bergthaller, « A quadratic equivalent of the minimum risk problem », Rev. Roum. Math. Pures et Appl., 15 (1970), 17-23. | MR 263424 | Zbl 0196.22901

[7] A. Charnes and W. W. Cooper, « Deterministic équivalents for optimizing and satisticing under chance constraints », Oper. Res. 11 (1963), 18-39. | MR 153482 | Zbl 0117.15403

[8] M. Dragomirescu, An algorithm for minimum risk solution of stochastic programming (to be published). | Zbl 0238.90053

[9] W. Fenchel, Convex cones, sets and functions, Princeton Univ., Princeton, 1953 (mimeographed). | Zbl 0053.12203

[10] A. M. Geoffrion, « Stochastic programming with aspiration or fracile criteria » Management Sci., 13 (1967), 672-679. | MR 242487 | Zbl 0171.17602

[11] M. Hanson, « Bounds for functionnaly convex optimal control problems », J. Matg. Anal. Appl., 8 (1964), 84-89. | MR 158797 | Zbl 0117.35601

[12] J.M. Henderson and R. Quandt, Microeconomic theory, Mc Graw-Hill, New York, London, 1958 | Zbl 0224.90014

[13] H. W. Kuhn and A. W. Tucker, Nonlinear programming, Proceed. Second Berkeley Symp. Math. Stat. Prob., Univ. Of California Press, Berkeley, 1951, 481-492. | MR 47303 | Zbl 0044.05903

[14] S. Karamardian, « Strictly quasi-convex (concave) functions and duality in mathematical programming », J. Math. Anal. Appl., 20 (1967), 344-358. | MR 219315 | Zbl 0157.49603

[15] S. Kataoka, « Stochastic programming. Maximum probality model », Hitotsubashi J. Arts Sciences, 8 (1967), 51-59. | MR 233587 | Zbl 0125.09601

[16] O. Mangasarian, « Pseudo-convex functions », J. Siam Control, 8 (1965), 281-290. | MR 191659 | Zbl 0138.15702

[17] O. Mangasarian, « Convexity, pseudo-convexity and quasi-convexity of composite functions », Cahiers Centre d'Études Recherche Opér., 12 (1970). 114-122. | MR 285276 | Zbl 0218.90042

[18] B. Martos. « Quasi-convexity and quasi-monotonicity in non-linear programming », Studia Sci. Math. Hungarica, 2 (1967), 265-273. | MR 224375 | Zbl 0178.22901

[19] A. Prekopa, Programming under probabilistic constraints and programming under constraints involving conditional expectations, 7th Mathematical Programming Symposium 1970, Abstracts, 107-109, North-Holland Amsterdam 1970.

[20] P. A. Samuelson, Foundations of economic analysis, Harvard Univ. Press, Cambridge, 1963. | MR 29145 | Zbl 0031.17401

[21] J. Stoer and C. Witzgall, Convexity and optimization in finite dimensions I, Springer, New York, Berlin, 1970. | MR 286498 | Zbl 0203.52203