kkt system – Optimization Online

Convergence Conditions for Newton-type Methods Applied to Complementarity Systems with Nonisolated Solutions

Published: 2015/01/15, Updated: 2015/09/01

Complementarity and Variational Inequalities, Nonlinear Optimization complementarity condition, constrained equation, constrained levenberg-marquardt method, error bound, generalized nash equilibrium problem, kkt system, lp-newton method

We consider a class of Newton-type methods for constrained systems of equations that involve complementarity conditions. In particular, at issue are the constrained Levenberg–Marquardt method and the recently introduced Linear Programming-Newton method, designed for the difficult case when solutions need not be isolated, and the equation mapping need not be differentiable at the solutions. We … Read more

ON REGULARITY CONDITIONS FOR COMPLEMENTARITY PROBLEMS

Published: 2012/02/28

Alexey F. Izmailov

A. S. Kurennoy

Complementarity and Variational Inequalities b-regularity, bd-regularity, cd-regularity, fischer-burmeister function, kkt system, mixed complementarity problem, natural residual function, nonlinear complementarity problems, quasi-regularity, semistability, strong regularity

In the context of mixed complementarity problems, various concepts of solution regularity are known, each of them playing a certain role in related theoretical and algorithmic developments. In this note, we provide the complete picture of relations between the most important regularity conditions for mixed complementarity problems. A special attention is paid to the particular … Read more

An LP-Newton Method: Nonsmooth Equations, KKT Systems, and Nonisolated Solutions

Published: 2011/09/22, Updated: 2013/03/14

Francisco Facchinei

Andreas Fischer

Markus Herrich

Complementarity and Variational Inequalities, Nonlinear Optimization kkt system, newton method, nonisolated solution, nonsmooth system, quadratic convergence

We define a new Newton-type method for the solution of constrained systems of equations and analyze in detail its properties. Under suitable conditions, that do not include differentiability or local uniqueness of solutions, the method converges locally quadratically to a solution of the system of equations, thus filling an important gap in the existing theory. … Read more

On mutual impact of numerical linear algebra and large-scale optimization with focus on interior point methods

Published: 2008/03/12

Marco D'Apuzzo

Valentina De Simone

Daniela di Serafino

Constrained Nonlinear Optimization adaptive stopping criteria, constraint preconditioners, inertia control, interior point methods, kkt system, large-scale optimization

The solution of KKT systems is ubiquitous in optimization methods and often dominates the computation time, especially when large-scale problems are considered. Thus, the effective implementation of such methods is highly dependent on the availability of effective linear algebra algorithms and software, that are able, in turn, to take into account specific needs of optimization. … Read more