conv5.mod: Gurobi complains that quadratic objective is not positive definite.

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5.3

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Xpress

conv6.mod: Xpress complains that quadratic objective is not conves.

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5.4

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SCIP

conv7.mod: optimal solution found (0,-2.5).

Original problem with (convex) quadratic constraints.

conv8.mod: optimal solution found, (0,1).

There is another solution in (0,-1) (the problem is non-convex).

Problem with non-convex feasible set.

conv9.mod: optimal solution found (0,1.73).

There is another solution in (0,-1.73) (the problem is non-convex).

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5.5

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See svm.mod.

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5.6

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See mdr.m.

You need to double the number of variables, since now for each x_i there are x_i^+ (that is equal to x_i if x_i>0 and equal to 0 otherwise), and x_i^- (that is equalt to 0 if x_i>0 and equal to -x_i otherwise).