Solve multivariable nonlinear equation with mixed constraints?

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How do I solve a

  • multivariable ($x_1$ to $x_m$)
  • nonlinear (in this case a quadratic)

objective function with mixed

  • (equality (my Sum) and
  • inequality (bounded variables)
  • in this case linear

constraints?

Is Lagrange an option here? (I know Lagrange can handle the equality constraints, but in combination with inequality constraints?)

Any help is apprecciated.