An interval algorithm for constrained global optimization
An interval arithmetic method for solving the global constrained problem \(\min f(x)\), \(g(x)= 0\), \(h(x)\leq 0\) is presented which shows the following features: (i) The problem is transformed to a penalty approach, \(\min F(x)\) with \(F= f+ cp\) and \(c\) being the penalty factor and \(p\) the \(L_ 1\)-exact penalty term. (ii) Numerical experience and computational results suggest the choice of a factor \(c\geq \bar c\), where \(\bar c= O(\max| f(x)|)\). Then the computation is rather insensitive to changes of \(c\). However, the value of \(\bar c\) has not been exploited completely yet. (iii) Additionally, infeasible areas \(Y\) are discarded during the computation using appropriate interval arithmetic exclusion tests.
scientific article; zbMATH DE number 643786