Adaptive partitioning strategies for solving multiextremal optimization problems

Following a brief introduction to the subject of multiextremal (global) optimization, a general class of direct (gradient-free) adaptive partition and search type solution strategies is considered. In an outline of the underlying main theoretical results, a prototype algorithmic framework is presented. This unifying approach subsumes e.g. a number of known one-dimensional global optimization methods; moreover, it has natural multivariate extensions and is implementable (in ‘tailored’ realizations) for handling continuous or Lipschitz-continuous objective functions defined on rectangular, convex, star-shaped or Lipschitzian nonconvex feasible sets. As some prospective applications of mutliextremal optimization, three important problem-types are investigated: the general solution of nonlinear equation systems, nonlinear model calibration and data classification (cluster analyses): numerical results are also presented.