In this paper we consider a mathematical program with second-order cone complementarity constraints (SOCMPCC). The SOCMPCC generalizes the mathematical program with complementarity constraints (MPCC) in replacing the set of nonnegative reals by a second-order cone. We show that if the SOCMPCC is considered as an optimization problem with convex cone constraints, then Robinson’s constraint quali...

The stabilized version of the sequential quadratic programming algorithm (sSQP) had been developed in order to achieve superlinear convergence in situations when the Lagrange multipliers associated to a solution are not unique. Within the framework of Fischer (Math Program 94:91–124, 2002), the key to local superlinear convergence of sSQP are the following two properties: upper Lipschitzian beh...

We introduce a twice differentiable augmented Lagrangian for nonlinear optimization with general inequality constraints and show that strict local minimizer of the original problem is an approximate solution Lagrangian. A novel method multipliers (ALM) then presented. Our originated from generalization Hestenes-Powell Lagrangian, combination interior-point technique. It shares similar algorithm...

Perturbations of Karush-Kuhn-Tucker conditions play an important role for primal-dual interior point methods. Beside the usual logarithmic barrier various further techniques of sequential unconstrained minimization are well known. However other than logarithmic embeddings are rarely studied in connection with Newton path-following methods. A key property that allows to extend the class of metho...

Abstract Linear bilevel optimization problems have gained increasing attention both in theory as well practical applications of Operations Research (OR) during the last years and decades. The latter is mainly due to ability this class model hierarchical decision processes. However, makes also very hard solve. Since no general-purpose solvers are available, a “best-practice” has developed applie...

We address the problem of preconditioning sequences of regularized KKT systems, such as those arising in interior point methods for convex quadratic programming. In this case, constraint preconditioners (CPs) are very effective and widely used; however, when solving large-scale problems, the computational cost for their factorization may be high, and techniques for approximating them appear as ...

Mathematical programs with equilibrium (or complementarity) constraints, MPECs for short, is a difficult class of constrained optimization problems. The feasible set has a very special structure and violates most of the standard constraint qualifications (CQs). Thus, the standard KKT conditions are not necessary satisfied by minimizers and the convergence assumptions of many standard methods fo...