pp-factor methods for nonregular inequality-constrained optimization problems

The paper presents a new method for solving irregular optimization problems with inequality constraints. Our results are based on the construction of pp-regularity theory and on reformulating the inequality constraints as equalities. Namely, by introducing the slack variables of corresponding degree we obtain the equality-constrained problem, where their gradients are linearly dependent, and for which the Lagrange optimality system is singular at the solution of the optimization problem. We have derived the pp-factor Lagrange system for finding extremum point x∗x∗, and under new sufficient condition of nondegeneracy in singular case we have proved regularity of this pp-factor Lagrange system at solution point (x∗,y∗,λ∗)(x∗,y∗,λ∗). At the end, we presented numerical scheme for general case.