@matbesancon You know what this legacy vs non-legacy interfaces is about?

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there was a change in the nonlinear API of JuMP. But it shouldn't change anything here if the user is just interacting with the CLI version of SCIP

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I provided the two .nl files in the original post. Have you confirmed the behavior that I observed in your versions of SCIP? I run SCIP by submitting the .nl files to COAP. https://www.coap.online/ When I submit the non-legacy .nl file to NEOS Knitro, Knitro seems to recognize the initial solution, as per the output below: "The initial point provided for the root node relaxation is feasible for the MIP and has obective value 1.020425e+04."

Artelys Knitro 14.0.0

concurrent_evals: 0
datacheck: 0
hessian_no_f: 1
numthreads: 4
Knitro changing mip_method from AUTO to 1.
Knitro changing mip_rootalg from AUTO to 1.
Knitro changing mip_lpalg from AUTO to 3.
Knitro changing mip_branchrule from AUTO to 2.
Knitro changing mip_selectrule from AUTO to 2.
Knitro changing mip_mir from AUTO to 2.
Knitro changing mip_clique from AUTO to 0.
Knitro changing mip_zerohalf from AUTO to 0.
Knitro changing mip_liftproject from AUTO to 0.
Knitro changing mip_knapsack from AUTO to 2.
Knitro changing mip_gomory from AUTO to 0.
Knitro changing mip_cut_flowcover from AUTO to 2.
Knitro changing mip_cut_probing from AUTO to 1.
Knitro changing mip_rounding from AUTO to 3.
Knitro changing mip_heuristic_strategy from AUTO to 1.
Knitro changing mip_heuristic_feaspump from AUTO to 1.
Knitro changing mip_heuristic_misqp from AUTO to 0.
Knitro changing mip_heuristic_mpec from AUTO to 1.
Knitro changing mip_heuristic_diving from AUTO to 0.
Knitro changing mip_heuristic_lns from AUTO to 0.
Knitro changing mip_heuristic_localsearch from AUTO to 1.
Knitro changing mip_pseudoinit from AUTO to 1.

Problem Characteristics ( Presolved)

Objective goal: Minimize
Objective type: general
Number of variables: 50 ( 50)
bounded below only: 0 ( 0)
bounded above only: 0 ( 0)
bounded below and above: 16 ( 16)
fixed: 0 ( 0)
free: 34 ( 34)
Number of binary variables: 16 ( 16)
Number of integer variables: 0 ( 0)
Number of constraints: 34 ( 34)
linear equalities: 34 ( 34)
quadratic equalities: 0 ( 0)
gen. nonlinear equalities: 0 ( 0)
linear one-sided inequalities: 0 ( 0)
quadratic one-sided inequalities: 0 ( 0)
gen. nonlinear one-sided inequalities: 0 ( 0)
linear two-sided inequalities: 0 ( 0)
quadratic two-sided inequalities: 0 ( 0)
gen. nonlinear two-sided inequalities: 0 ( 0)
Number of nonzeros in Jacobian: 578 ( 578)
Number of nonzeros in Hessian: 51 ( 51)

Knitro using Branch and Bound method with 4 threads.

Initial points

The initial point provided for the root node relaxation is feasible for the MIP and has obective value 1.020425e+04.
No primal point provided for the MIP.

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The .nl reader of SCIP needs to reformulate a nonlinear objective function into a constraint, since SCIP does not support nonlinear objective functions. For that, it introduces a new variable, nlobjvar. Unfortunately, it does not calculate a value for this variable for the initial solution. I will take a look whether that is possible.

The legacy and non-legacy model seem to be very different - different variables and different constraints. I suppose they only equivalent after aggregating the continuous variables.
In the legacy model, the objective function is already reformulated as constraints, and I suppose a corresponding initial value has been set for the continuous variable that has been introduced for that purpose.

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Yes, ignore the "legacy" stuff. It has nothing to do with this issue. (See discussion https://discourse.julialang.org/t/legacy-vs-non-legacy-jump-nonlinear-model-nl-files-with-initial-solution/115442)

since SCIP does not support nonlinear objective functions. For that, it introduces a new variable, nlobjvar. Unfortunately, it does not calculate a value for this variable for the initial solution

This sounds right and matches up with the error message:

 [nonlinear] <objcons>: ((1*(<x0>*<x0>)+1*(<x17>*<x17>)+(-0.5)))^2+((1*(<x1>*<x1>)+1*(<x18>*<x18>)+(-0.5)))^2+((1*(<x2>*<x2>)+1*(<x19>*<x19>)+(-0.5)))^2+((1*(<x3>*<x3>)+1*(<x20>*<x20>)+(-0.5)))^2+((1*(<x4>*<x4>)+1*(<x21>*<x21>)+(-0.5)))^2+((1*(<x5>*<x5>)+1*(<x22>*<x22>)+(-0.5)))^2+((1*(<x6>*<x6>)+1*(<x23>*<x23>)+(-0.5)))^2+((1*(<x7>*<x7>)+1*(<x24>*<x24>)+(-0.5)))^2+((1*(<x8>*<x8>)+1*(<x25>*<x25>)+(-0.5)))^2+((1*(<x9>*<x9>)+1*(<x26>*<x26>)+(-0.5)))^2+((1*(<x10>*<x10>)+1*(<x27>*<x27>)+(-0.5)))^2+((1*(<x11>*<x11>)+1*(<x28>*<x28>)+(-0.5)))^2+((1*(<x12>*<x12>)+1*(<x29>*<x29>)+(-0.5)))^2+((1*(<x13>*<x13>)+1*(<x30>*<x30>)+(-0.5)))^2+((1*(<x14>*<x14>)+1*(<x31>*<x31>)+(-0.5)))^2+((1*(<x15>*<x15>)+1*(<x32>*<x32>)+(-0.5)))^2+((1*(<x16>*<x16>)+1*(<x33>*<x33>)+(-0.5)))^2-<nlobjvar> <= 0;
violation: right hand side is violated by 10204.25
all 1 solutions given by solution candidate storage are infeasible

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