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You can use BARON and Knitro for free from the NEOS Server. Also, you have the following options:
If you are in the first year of graduation, you can apply for a one-year free graduate student license of AMPL which includes both solvers.
If you are an individual with a CMU or UIUC email address or related to sponsors of the CAPD you can have a free academic ...
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The McCormick envelope is one possible approach. Another, if the domain of $y$ is not too large, is to use a type 1 Special Ordered Set. Assume that $y\in\lbrace 1,\dots,N\rbrace$. Replace $y$ with$$\sum_{j=1}^N j\cdot z_j$$where the $z_j$ are binary variables, and replace the equation $xy=q$ with$$x=\sum_{j=1}^N\frac{q}{j}z_j.$$Add the constraint$$\sum_{j=1}...
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You can also download our Octeract Engine - it's free for students and academic staff and solves a superset of the problem types that BARON and KNITRO do (global optimality for non convex problems + trigonometric & nonsmooth & discontinuous problems).
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BARON is having trouble finding a feasible local solution.
The $0.100000E+52$ number is the default number used before the first feasible solution is found.
The word "scaled" can be misleading here, Clp's output hints that your model's constraints are likely overdefined, which causes numerical instability in both the linear and non-linear solvers.
The ...
1
If a deterministic global optimisation solver (such as Baron) reports a local solution, that solution is reliable. If the solver is terminated prematurely, the global solver will return the best solution it has found so far.
For NLP, it is quite common that global solvers find the global solution very early on, and then spend the majority of time proving it ...
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By reading your edited question, I think you are trying to get feasible solutions(values for the variables that satisfy the system of equations). If it's true, you can simply fix the objective function and use BARON to get the values for the variables. In PYOMO:
from pyomo.util.infeasible import log_infeasible_constraints
# ...your model M...
# ...Lines of ...
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