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I was reading this paper related to Multiclass Classification with Multi-Prototype Support Vector Machines - paper

However, I am having difficulty in understanding why they have mentioned the following problem non convex.

I am really struggling figuring out the convexity/concavity of the functions. Can anyone just skim through the paper to help me out. The paper is about SVM (multi class classification) where each class can have multiple weight vectors/prototypes.

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    $\begingroup$ Welcome to SciComp! I've noticed a pattern with your questions: almost all of them are about SVM, and frequently, they devolve into "I don't understand this paper." These questions are valid. They are also likely to remain unanswered for quite some time because the way they're posed requires someone unfamiliar with the paper to read it and understand it at a fairly deep level, and it's unlikely that people visiting your question are going to read the paper if they haven't already. I urge you to formulate your questions so that a broader audience of people can answer them. $\endgroup$ – Geoff Oxberry Mar 14 '13 at 4:51
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Sounds too simple so maybe I've misunderstood you, but they have binary variables, hence obviously a nonconvex problem (a binary variable is either 0 or 1, which is a nonconvex set)

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  • $\begingroup$ This was my first thought exactly. In this case, because the problem is mixed-integer, it doesn't matter that any of the other functions are convex or nonconvex. $\endgroup$ – Geoff Oxberry Mar 14 '13 at 16:38
  • $\begingroup$ @Geoff Oxberry. I didn't get what you mean by mixed-integer $\endgroup$ – user34790 Mar 15 '13 at 3:53
  • $\begingroup$ @user34790: Integer programs have decision variables that are restricted to integer values. Mixed-integer programs have both integer and continuous variables, like the optimization formulation you have posted above. $\endgroup$ – Geoff Oxberry Mar 15 '13 at 4:00

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