The Montagnes Russes algorithm for global optimization

The ‘Montagnes Russes’ algorithm for finding the global minima of a lower semi-continuous function (thus involving state constraints) is a descent algorithm applied to an auxiliary function whose local and global minima are the global minima of the original function. Although this auxiliary function decreases along the trajectory of any of its minimizing sequences, the original function jumps above local maxima, leaves local minima, playing ‘Montagnes Russes’ (called ‘American Mountains’ in Russian and ‘Big Dipper’ in American!), but, ultimately, converges to its infimum. This auxiliary function is approximated by an increasing sequence of functions defined recursively at each point of the minimizing sequence.