We propose a new set of preconditioners for the iterative solution, via a Preconditioned Conjugate Gradient (PCG) method, of the KKT systems that must be solved at each iteration of an Interior Point (IP) algorithm for the solution of linear Min Cost Flow (MCF) problems. These preconditioners are based on the idea of extracting a proper triangulated subgraph of the original graph which strictly...

Variational inequalities over sets deened by systems of equalities and inequalities are considered. A continuously diierentiable merit function is proposed whose unconstrained minima coincide with the KKT-points of the variational inequality. A detailed study of its properties is carried out showing that under mild assumptions this reformulation possesses many desirable features. A simple algor...

We address the iterative solution of symmetric KKT systems arising in the solution of convex quadratic programming problems. Two strictly related and well established formulations for such systems are studied with particular emphasis on the effect of preconditioning strategies on their relation. Constraint and augmented preconditioners are considered, and the choice of the augmentation matrix i...

This paper presents an electrical impedance tomography (EIT) method using a partial-differential-equation-constrained optimization approach. The forward problem in the inversion framework is described by complete electrode model (CEM), which seeks electric potential within domain and at surface electrodes considering contact between them. finite element solution of has been validated commercial...

The aim of the paper is to provide a theoretical basis for approximate reduced SQP methods. In contrast to inexact reduced SQP methods, the forward and the adjoint problem accuracies are not increased when zooming in to the solution of an optimization problem. Only linear-quadratic problems are treated, where approximate reduced SQP methods can be viewed as null-space iterations for KKT systems...

For an inequality system defined by an infinite family of proper convex functions (not necessarily lower semicontinuous), we introduce some new notions of constraint qualifications. Under the new constraint qualifications, we provide necessary and/or sufficient conditions for the KKT rules to hold. Similarly, we provide characterizations for constrained minimization problems to have total Lagra...

We propose a variant of the classical augmented Lagrangian method for constrained optimization problems in Banach spaces. Our theoretical framework does not require any convexity or second-order assumptions and allows the treatment of inequality constraints with infinite-dimensional image space. Moreover, we discuss the convergence properties of our algorithm with regard to feasibility, global ...

Constraint qualifications (CQ) are assumptions on the algebraic description of the feasible set of an optimization problem that ensure that the KKT conditions hold at any local minimum. In this work we show that constraint qualifications based on the notion of constant rank can be understood as assumptions that ensure that the polar of the linear approximation of the tangent cone, generated by ...

Computing the chromatic number of a graph is an NP-hard problem. For random graphs and some other classes of graphs, estimators of the expected chromatic number have been well studied. In this paper, a new 0–1 integer programming formulation for the graph coloring problem is presented. The proposed new formulation is used to develop a method that generates graphs of known chromatic number by us...