A semistrong sufficiency condition for optimality in nonconvex programming and its connection to the perturbation problem (Q1095037)

What happens when a nonconvex program, having a local solution \(x^ 0\) at which the gradients of the binding constraints are linearly independent, but without strict complementarity hypothesis, is perturbed? Under a relatively weak second-order assumption (some nonnegative second- order terms is supposed to be strictly positive), the perturbed problem has, in the neighborhood of \(x^ 0\), a finite number of local minima, situated on curves that are connected to some pseudo-solutions of the tangent quadratic problem.