On existence of solutions to degenerate nonlinear optimization problems
Agnieszka Prusińska, Alexey A Tret’yakov · Discussiones Mathematicae Differential Inclusions Control and Optimization · 2007
We investigate the existence of the solution to the following problem min ’(x) subject to G(x) = 0; where ’ : X ! R; G : X ! Y and X; Y are Banach spaces. The question of existence is considered in a neighborhood of such point x0 that the Hessian of the Lagrange function is degenerate. There was obtained an approximation for the distance of solution x to the initial point x0: