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Articles, 4 records found
Articles 4 records found  
11 p, 351.0 KB Weakly Motzkin Predecomposable Sets / Martínez Legaz, Juan Enrique (Universitat Autònoma de Barcelona. Departament d'Economia i d'Història Econòmica) ; Todorov, M. I. (Universidad de las Américas)
We introduce and study the class of weakly Motzkin predecomposable sets, which are those sets in ℝ n that can be expressed as the Minkowski sum of a bounded convex set and a convex cone, none of them being necessarily closed. [...]
2017 - 10.1007/s11228-017-0420-0
Set-Valued and Variational Analysis, Vol. 25, Núm. 3 (September 2017) , p.507-516  
15 p, 319.5 KB Motzkin predecomposable sets / Iusem, N. (Instituto de Matématica Pura e Aplicada) ; Martínez Legaz, Juan Enrique (Universitat Autònoma de Barcelona. Department d'Economia i d'Història Econòmica) ; Todorov, Maxim Ivanov (Universidad de las Américas. Departmento de Actuaría y Matemáticas)
We introduce and study the family of sets in a finite dimensional Euclidean space which can be written as the Minkowski sum of a compact and convex set and a convex cone (not necessarily closed). We establish several properties of the class of such sets, called Motzkin predecomposable, some of which hold also for the class of Motzkin decomposable sets (i. [...]
2014 - 10.1007/s10898-013-0097-3
Journal of Global Optimization, Vol. 60, Núm. 4 (2014) , pp. 635–647  
14 p, 612.0 KB Perturbation analysis of a condition number for convex inequality systems and global error bounds for analytic systems / Sien, Deng
In this paper several types of perturbations on a convex inequality system are considered, and conditions are obtained for the system to be well-conditioned under these types of perturbations, where the well-conditionedness of a convex inequality system is defined in terms of the uniform boundedness of condition numbers under a set of perturbations. [...]
Mathematical Programming, vol. 83 n. 2 (1998) p. 263-276  
 UAB restricted access
20 p, 1010.2 KB First and second order analysis of nonlinear semidefinite programs / Shapiro, Alexander
In this paper we study nonlinear semidefinite programming problems. Convexity, duality and first-order optimality conditions for such problems are presented. A second-order analysis is also given. Second-order necessary and sufficient optimality conditions are derived. [...]
Mathematical Programming, vol. 77 n. 2 (1997) p. 301-320  
 UAB restricted access

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