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The facial reduction algorithm of Borwein and Wolkowicz and the extended dual of Ramana provide a strong dual for the conic linear program $$ (P) \sup {<c, x> | Ax \leq_K b} $$ in the absence of any constraint qualification.
Convex Analysis
Tyrrel R. Rockafellar · 1970
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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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Robert M. Freund, Robin Roundy, and Michael J. Todd · 1985
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Robert M. Freund · 1994
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Motakuri V. Ramana · 1997
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