An algorithm based on continuation techniques for minimization problems with highly non-linear equality constraints

Understand

We present an algorithm based on continuation techniques that can be applied to solve numerically minimization problems with equality constraints.

• We focus on problems with a great number of local minima which are hard to obtain by local minimization algorithms with random starting guesses.
• We are particularly interested in the computation of minimal norm solutions of underdetermined systems of polynomial equations.
• Such systems arise, for instance, in the context of the construction of high order optimized differential equation solvers.