For all solvers, the solution for the x_2 component is inaccurate.

Using KNITRO and the suggested option, the accuracy is to machine precision.

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2.2

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There are at least two solutions, one for the suggested starting guess ( x_i = 1 / n ) and one for x_i = (-1)^i / n

Both solutions have the same objective, i.e. 0.

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2.3

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Most of solvers give very bad fits. Only CONOPT gives the same solution as the certified values.

The problem is ill-conditioned, with 9 orders of magnitude between the largest and the smallest coefficients.

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2.4

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Orthogonal distance regression improves the solution for most solvers (in that the residuals are smaller), but still CONOPT is the only one getting the same solution as the certified values.