Geodesic
Quadratic forms positive on the cone and quadratic duality
Zapiski Nauchnykh Seminarov POMI, Automorphic functions and number theory. Part II, Tome 134 (1984), pp. 59-83

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A general pattern is outlined for the study of quadratic forms which are positive on a cone in a finite-dimensional linear space. Quadratic duality theorems are proved. An example related to the $S$-procedure in controle theory and to the Pareto-optimum is thoroughly considered. Geometric proof of the Hausdorff–Toeplitz convexity theorem is discussed. 
@article{ZNSL_1984_134_a3,
     author = {A. M. Vershik},
     title = {Quadratic forms positive on the cone and quadratic duality},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {59--83},
     publisher = {mathdoc},
     volume = {134},
     year = {1984},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1984_134_a3/}
}
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A. M. Vershik. Quadratic forms positive on the cone and quadratic duality. Zapiski Nauchnykh Seminarov POMI, Automorphic functions and number theory. Part II, Tome 134 (1984), pp. 59-83. http://geodesic.mathdoc.fr/item/ZNSL_1984_134_a3/