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Dear SCIP team,</div>
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I am trying to solve a relatively simple convex MINLP of the shape:</div>
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min c^t x</div>
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s.t.: g_i(x,y) \leq 0 i \in 1..m</div>
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Ax + By \leq d</div>
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x \in R^n, y \in B^n' </div>
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with all functions g_i convex (cf "Convex MINLP" in <a href="https://www.scipopt.org/doc/html/WHATPROBLEMS.php">
https://www.scipopt.org/doc/html/WHATPROBLEMS.php</a> ).</div>
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I try to solve the MINLP (with variables y in {0,1}, and its convex relaxation (with variables y in [0,1] ).</div>
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In the documentation, a parameter "constraints/nonlinear/assumeconvex" is described, which allows assuming that all constraint functions are convex.</div>
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The convex relaxed NLP with y \in [0,1]: </div>
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<div class="elementToProof" role="presentation">is easily solved by SCIP when the "constraints/nonlinear/assumeconvex" parameter equals TRUE</div>
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<div class="elementToProof" role="presentation">is not easily solved by SCIP (several minutes for a toy instance with a few variables and constraints) when "constraints/nonlinear/assumeconvex" equals FALSE ; from the logs, it seems SCIP can't prove the complexity
of the constraints and runs a spatial branch-and-bound (several nodes are generated, despite having only continuous variables).</div>
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The MINLP with y \in {0,1}:</div>
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<div class="elementToProof" role="presentation">is not correctly solved when "constraints/nonlinear/assumeconvex" is true: a feasible solution, with values of the binary variable y fixed "randomly", is returned by SCIP.</div>
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<div class="elementToProof" role="presentation">is very slow when "constraints/nonlinear/assumeconvex" is false</div>
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So it seems the "constraints/nonlinear/assumeconvex" parameters not only controles the convexity of the constraints in the NLP relaxation, but also the convexity of the variables' domains - which would make it improper to solve an MINLP.</div>
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Is this understanding correct and, if so, is there a way to solve a MINLP when all constraints are known to be convex - but the variables domain isn't ? (for instance by stating, for each nonlinear constraint, that it should be considered as convex?)</div>
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Many thanks,</div>
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Guilaume</div>
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