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We study the boundary structure of closed convex cones, with a focus on facially dual complete (nice) cones.
Convex analysis
R. Tyrrell Rockafellar · 1970
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Facial reduction for a cone-convex programming problem
Jon M. Borwein and Henry Wolkowicz · 1980
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Fundamentals of convex analysis
Jean-Baptiste Hiriart-Urruty and Claude Lemaréchal · 1993
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Analysis on symmetric cones
Jacques Faraut and Adam Korányi · 1994
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Hyperbolic polynomials and interior point methods for convex programming
Osman Güler · 1997
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An exact duality theory for semidefinite programming and its complexity implications
Motakuri V. Ramana · 1997
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Variational analysis
R. Tyrrell Rockafellar and Roger J.-B. Wets · 1998
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On homogeneous convex cones, the Carathéodory number, and the duality mapping
Levent Tunçel and Song Xu · 2001
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Geometry of homogeneous convex cones, duality mapping, and optimal self-concordant barriers
Van Anh Truong and Levent Tunçel · 2004
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Lexicographic differentiation of nonsmooth functions
Yu. Nesterov · 2005
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Hyperbolic programs, and their derivative relaxations
James Renegar · 2006
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On the closedness of the linear image of a closed convex cone
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Invariance and efficiency of convex representations
Chek Beng Chua and Levent Tunçel · 2008
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Semidefinite facial reduction for low-rank euclidean distance matrix completion
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Euclidean distance matrices and applications
Nathan Krislock and Henry Wolkowicz · 2012
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Strong duality and minimal representations for cone optimization
Levent Tunçel and Henry Wolkowicz · 2012
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Basis selection for SOS programs via facial reduction and polyhedral approximations
Frank Permenter and Pablo A Parrilo · 2014
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Facially exposed cones are not always nice
Vera Roshchina · 2014
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Coordinate shadows of semidefinite and Euclidean distance matrices
Dmitriy Drusvyatskiy, Gábor Pataki, and Henry Wolkowicz · 2015
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Exact duality in semidefinite programming based on elementary reformulations
Minghui Liu and Gábor Pataki · 2015
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Facial reduction and partial polyhedrality
Bruno F Lourenço, Masakazu Muramatsu, and Takashi Tsuchiya · 2015
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Solving conic optimization problems via self-dual embedding and facial reduction: a unified approach
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Lifts of convex sets and cone factorizations
João Gouveia, Pablo A. Parrilo, and Rekha R. Thomas · 2013
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On the connection of facially exposed and nice cones
Gábor Pataki · 2013
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Strong duality in conic linear programming: facial reduction and extended duals
Gábor Pataki · 2013
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Preprocessing and reduction for semidefinite programming via facial reduction: Theory and practice
Yuen-Lam Cheung (Vris Voronin) · 2013
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Facial reduction algorithms for conic optimization problems
Hayato Waki and Masakazu Muramatsu · 2013
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Frank Permenter, Henrik A Friberg, and Erling D Andersen · 2015
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Variational analysis of regular mappings
Alexander D. Ioffe · 2017
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Bruno F. Lourenço · 2017
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