Recent developments in constrained optimization (Q1112728)

This is a survey paper, discussing a number of techniques for constrained optimization and highlighting some more recent developments. The problem under consideration consists in minimizing F(x) subject to c(x)\(\geq 0\) where F: \(R^ n\to R^ 1\) and c: \(R^ n\to R^ m\) have continuous second derivatives, at least in a neighbourhood of the solution. The older methods outlined in the paper include penalty-function methods, barrier-function methods, and generalized reduced gradient methods. Three sections deal with Lagrange functions (properties of the Lagrangian functions, augmented Lagrangian methods, projected Lagrangian methods), and two sections deal with sequential quadratic programming methods. The last two sections are devoted to methods for large-scale optimization and to the optimal power flow problem. 50 references are given.