Estimation of Lipschitzian Problem Characteristics in Global Optimization

Abstract

We shall consider again the Lipschitz global optimization problem on a finite n-interval [a, b]:

$$\begin{array}{*{20}{c}} {\min f(x)}\\ {a \le x \le b,\quad a,x,b \in {R^n}} \end{array}$$

(3.3.2)

under the analytical conditions stated in Chapter 2.4; in particular, f is assumed to be Lipschitz-continuous with some constant L. As previously, the—not necessarily unique—optimal solution of this LGOP will be denoted by x* ∈ X*, and f* = f(x*). Additionally, the set of accumulation points generated by a PAS-type globally convergent adaptive partition algorithm will be denoted again by X ^a.