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Conic linear programs, among them semidefinite programs, often behave pathologically: the optimal values of the primal and dual programs may differ, and may not be attained.
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On point classification in convex sets
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Facial reduction for a cone-convex programming problem
Jonathan M. Borwein and Henry Wolkowicz · 1981
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Regularizing the abstract convex program
Jonathan M. Borwein and Henry Wolkowicz · 1981
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Duality in semi-infinite linear programming
Richard Duffin, Robert Jeroslow, and Les A. Karlovitz · 1983
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Convex Analysis and Minimization Algorithms
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Closedness criteria for the image of a closed set by a linear operator
Alfred Auslender · 1996
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On the ELSD duality theory for SDP
Motakuri V. Ramana and Robert Freund · 1996
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Duality results for conic convex programming
Zhi-Quan Luo, Jos Sturm, and Shuzhong Zhang · 1997
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An exact duality theory for semidefinite programming and its complexity implications
Motakuri V. Ramana · 1997
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Strong duality for semidefinite programming
Motakuri V. Ramana, Levent Tunçel, and Henry Wolkowicz · 1997
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Complexity and Real Computation
Lenore Blum, Felipe Cucker, Michael Shub, and Stephen Smale · 1998
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Conical open mapping theorems and regularity
Heinz Bauschke and Jonathan M. Borwein · 1999
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Perturbation analysis of optimization problems
Frédéric J. Bonnans and Alexander Shapiro · 2000
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Convex Analysis and Nonlinear Optimization: Theory and Examples
Jonathan M. Borwein and Adrian S. Lewis · 2000
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The geometry of semidefinite programming
Gábor Pataki · 2000
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Lectures on modern convex optimization
Aharon Ben-Tal and Arkadii Nemirovskii · 2001
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A Mathematical View of Interior-Point Methods in Convex Optimization
James Renegar · 2001
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Semidefinite optimization
Michael J. Todd · 2001
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Notes on duality in second order and p p -order cone optimization
Erling D. Andersen, Cees Roos, and Tamás Terlaky · 2002
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A Course in Convexity
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Hua Wei and Henry Wolkowicz · 2010
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Convex Analysis and Monotone Operator Theory in Hilbert Spaces
Heinz Bauschke and Patrick Combettes · 2011
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Polyhedral and Semidefinite Programming Methods in Combinatorial Optimization
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Immanuel Bomze, W. Schachinger, and G. Uchida · 2012
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Strong duality and minimal representations for cone optimization
Levent Tunçel and Henry Wolkowicz · 2012
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Alexander Barvinok · 2002
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Relating homogeneous cones and positive definite cones via T-algebras
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Set intersection theorems and existence of optimal solutions
Dimitri Bertsekas and Paul Tseng · 2007
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On the closedness of the linear image of a closed convex cone
Gábor Pataki · 2007
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Universal duality in conic convex optimization
Simon P. Schurr, André L. Tits, and Dianne P. O’Leary · 2007
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Coordinate shadows of semi-definite and euclidean distance matrices
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