Let $K$ be a convex cone which is not closed. The look at a probem of the from $$\min <C,X>, \,s.t\; <A_i,X>=b_i,\, X\in C.$$ Now suppose I now that both this program and its dual have a strictily feasable point. Does then strong duality apply? In particular does this mean that the set of optimal points is compact?
2026-04-11 15:50:23.1775922623
Strong duality in conic programmig
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