Bounds for Lagrange multipliers and optimal points (Q1802498)

The following optimization problem is considered: Minimize \(f(x)\) subject to \(p_ i(x)\leq 0\) \((i= 1,\dots,m)\), \(q_ i(x)=0\) \((i=1,\dots,r)\), where \(f\), \(p_ i\), \(q_ i\) are given functions from class \(C^ 2\) defined on \(\mathbb{R}^ n\). Using the Fritz-John conditions the authors describe two methods for computing guaranteed bounds on the Lagrange multipliers. The first of the two methods makes possible to compute also guaranteed bounds on the location of the optimal points.