On reductibility of degenerate optimization problems to regular operator equations (Q518575)

The authors investigate degenerate equality constrained optimization problems on Banach spaces; by degeneracy they mean that the derivative of the constraint function at a solution is not surjective. To reduce such problems to regular systems of equations, they use the \(p\)-regularity theory due to \textit{A. A. Tret'yakov} [Zh. Vychisl. Mat. Mat. Fiz. 24, No. 2, 203--209 (1984; Zbl 0537.49009); Russ. Math. Surv. 42, No. 5, 179--180 (1987; Zbl 0683.58008); translation from Usp. Mat. Nauk 42, No. 5(257), 215--216 (1987)]. The systems so obtained do not involve the objective functions, and their solutions are proved to be locally unique. Applications to mathematical programming problems with complememtarity constraints and to linear programming problems are discussed.