Abstract
Many problems of optimization involve the minimization of an objective function on a convex cone. In this respect we define a concave gauge function which will be used in interior point methods.
Application are given in particular on the space of real symmetric matrices.
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References
Balan TT (1970) Observatii asupra functionalelor supra-aditive. Analele Univ. Craiova 1
Balan TT (1992) Generaling the Minkowski space-time (I) and (II). Stud Cerc Math Tom 44, 2:89–107
Ball JM (1976–77) Convexity conditions and existance theorems in nonlinear elasticity. Arch Rat Mech Anal 63:337–403
Birkhoff G (1946) Tres observationes sobre el algebra lineal. Revista Facultad de Ciencias Exactas, Puras y Applicadas Universidad National de Tucuman, Serie A (Mathematicas y Fisica Teorica) 5:147–151
Calvaire B (1991) Strictly plus functionals on a super-additive normed linear space, Technical paper, Aucland University
Calvaire B, Fitzpatrick S Characterizing Lorenz space by norm one projections. To appear in Studia Scient Math Hungarica
Crouzeix JP (1980) Condition for convexity of quasiconvex functions. Mathematics of Operation Research 5, 1:120–125
Crouzeix JP, Ferland JA, Schaible S (1992) Generalized convexity of functions on affine subspaces with an application to potential functions. Mathmeatical Programming 56:223–232
Crouzeix JP, Lindberg PO (1986) Additively decomposed quasiconvex functions. Mathematical Programming 35:42–57
Debreu G, Koopmans TC (1982) Additively decomposed quasiconvex functions. Mathematical Programming 23:193–205
Gaffke N, Krafft O (1982) Matrix inequalities in the löwner ordering. Modern Applied Mathematics-Optimisation and Operation Research Körte B. North-Holland Publishing Company 595–622
Haynsworth EV (1968) Determination of the inertia of a partitioned Hermitian matrix. Linear Algebra and Applications 1:73–81
Marques MDPM, Moreau JJ (1982) Isotropie et convexité dans l'espace des tenseurs symê-triques. Travaux du Séminaire d'Analyse Convexe, Montpellier 12, 6
Magnus JR, Neudecker H (1988) Matrix differential calculus with applications in statistics and econometrics. John Wiley & Sons 198–239
Von Neumann J (1953) A certain zero-sum two-person game equivalent to the optimal assignment problem. In: Kuhn HW, Tucker AW (eds) Contribution to the Theory of Games II. Annals of Mathematics Studies 28:5–12
Newman P (1969) Some properties of concave functions. Journal Econom Theory 1:291–314
Ruys PHM, Weddepohl HN (1979) Economic theory and duality. Lecture notes in Economics and Mathematical systems, No. 168. Jacobus Kriens Springer-Verlag, Berlin-Heidelberg-New York 49–72
Tind J (1974) Blocking and antiblocking sets. Mathematical Programming 6:157–166. North-Holland Publishing Company
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Barbara, A., Crouzeix, J.P. Concave gauge functions and applications. ZOR - Methods and Models of Operations Research 40, 43–74 (1994). https://doi.org/10.1007/BF01414029
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DOI: https://doi.org/10.1007/BF01414029