Geometric notes on optimization with equality constraints Original Research Article

For minimization problems with nonlinear equality constraints, various numerical tools are shown to become available when the constraint set has a manifold structure. In appropriate local coordinate systems these tools permit the computation, e.g., of the gradient and Hessian of the transformed (unconstrained) objective function. This opens up a new view on the computational solution of the minimization problem which—while leading to algorithms similar in concept and performance to the well-known “reduced Hessian” methods—provides a different theoretical basis for these methods.