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- W3149289119 abstract "In their paper Duality of linear conic Shapiro and Nemirov- ski considered two possible properties (A) and (B) for dual linear conic problems (P) and (D). The property (A) is If either (P) or (D) is feasible, then there is no duality gap between (P) and (D), while property (B) is If both (P) and (D) are feasible, then there is no duality gap between (P) and (D) and the optimal values val(P) and val(D) are finite. They showed that (A) holds and the cone K is polyhedral, and gave some partial results related to (B). Later Shapiro conjectured that (B) holds and all the nontrivial faces of the cone K are polyhedral. In this note we mainly prove that both the and only if parts of this conjecture are not true by providing examples of closed convex cone in R 4 for which the corresponding implications are" @default.
- W3149289119 created "2021-04-13" @default.
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- W3149289119 date "2012-01-01" @default.
- W3149289119 modified "2023-09-27" @default.
- W3149289119 title "On duality gap in linear conic problems" @default.
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