Yuriy Zinchenko

Hello Mike,   The modelling approach will depend on whether you want to minimize or maximize your objective. For example, if you want to maximize, with r fixed, and v's being non-negative, to build...

This is not unexpected, Bruno.  Note if the solution limit is set to 1, the emphasis is really on funding at least one feasible solution, and Gurobi takes that into account.   Hope this helps.

Thanks for providing more details, and yes, I would try the re-scaling that was described earlier to see what happens.  For the linear term, I would apply the same change of variable and not worry ...

You can try experimenting with NodeMethod parameter, https://www.gurobi.com/documentation/9.0/refman/nodemethod.html as sometimes non-default setting (e.g., barrier) does better for certain models....

At every iteration of the barrier one solves a system of linear equations, and this is often the most expensive part.   >> the data structures that Gurobi uses, are sparse yes, you can think of it ...

QObjective range specifies the range of the matrix in the quadratic objective, and you can think of it as the Hessian of the objective as well.  The right hand side of the constraints is not necess...

This works for L-infinity norm:   maximize r subject to (***) \sum_j abs( A_{i,j} ) r  \leq b - A c   Since it is could be a bit tricky to figure out how to avoid checking 2^n vertices, I made it e...

For L1 norm you have a unit ball defined by |x| + |y| + |z| + ... <= 1 with respective vertices (1;0;0;....), (-1;0;0;...), (0;1;0;0...) etc.giving you 2n vertices in dimension n, whereas, the L-in...

ps: apparently I was thinking of L-\infintiy norm in |x' - x| = max_j |x_j - x_j'| \leq \delta in the above.   If you want the L1 norm, this should be easier, as you only need to check the containm...

With L1 norm in mind, I think one can give a nice compact formulation to this problem.  But please take it with a grain of salt, so to speak, as I did not test it, and read and check things careful...