Extended cutting angle method of global optimization

Methods of Lipschitz optimization allow one to find and confirm the global minimum of multivariate Lipschitz functions using a finite number of function evaluations. This paper extends the Cutting Angle method, in which the optimization problem is solved by building a sequence of piecewise linear underestimates of the objective function. We use a more flexible set of support functions, which yields a better underestimate of a Lipschitz objective function. An efficient algorithm for enumeration of all local minima of the underestimate is presented, along with the results of numerical experiments. One dimensional Pijavski-Shubert method arises as a special case of the proposed approach.