Iterative linearization in the method of barrier functions (Q1086168)

Consider the problem of finding the minimum of a function f(x) on a set X, where \(X=\{x\in E_ n:\) \(g_ i(x)\geq 0\), \(i=1,...,m\}\). To solve the problem we propose an iterative modification of the method of internal penalty functions, based on variation of the penalty parameter in the process of constructing a minimizing sequence. Or, in greater detail, for each fixed value of the penalty parameter \(\epsilon_ k\) we will confine ourselves to minimizing the principal linear part of the increment of the penalized function at point \(x_ k\) on a set of simple structure.