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I am studying the Duality Chapter of Convex Optimization by Boyd. Is it possible that strong duality holds for non-convex optimization? If yes, is there any specific condition? And, what is the relationship between Slater condition and strong duality? Based on the definition in the book, the Slater condition is vague to me. I would be thankful if you can explain it. In general, what are the relationship between KKT, strong duality, Slater condition, convex and non-convex optimization?

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  • $\begingroup$ Read en.wikipedia.org/wiki/Slater%27s_condition . That lays it out fairly clearly. And yes, strong duality can hold in non-convex optimization - for material on that, google strong duality non-convex $\endgroup$ – Mark L. Stone Mar 23 at 1:26
  • $\begingroup$ Thanks Mark. I am confused about the relationship between "KKT, strong duality, Slater condition, convex and non-convex optimization" and when KKT is sufficient and when it is necessary. Is there any reference which classifies them clearly? $\endgroup$ – Katatonia Mar 23 at 4:42

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