In my engineering application, all decision variables are non-negative and everything is convex separable. In addition to that, the only function that I am trying to approximate with grid point are $f(x)=x^3$ and $g(y)=y^4$.

I am having this strange feeling about solving separable programming problem. Particularly for imposing the following requirement on the $\lambda$.

  1. At most 2 $\lambda$ are positive
  2. They must be adjacent

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From what I know, this can be done by modifying the entering and leaving variable of the simplex tableu. However, if I am using an interior point method solver like MOSEK then how can I impose these constraint ?

  • 2
    $\begingroup$ You can solve the original nonlinear problem with Mosek. Most likely that is faster and easier. $\endgroup$ Apr 1 at 6:47
  • 2
    $\begingroup$ Btw conditions 1 and 2 do not have to be stated explicitly if the problem is convex IMO. $\endgroup$ Apr 2 at 7:49


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