On the resolution of monotone complementarity problems

DOI10.1007/BF00249054zbMath0859.90113OpenAlexW2140603012MaRDI QIDQ1815077

Carl Geiger, Christian Kanzow

Publication date: 3 November 1996

Published in: Computational Optimization and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00249054

zbMATH Keywords

unconstrained minimizationstationary pointsglobal minimadescent algorithmnonlinear complementarity

Mathematics Subject Classification ID

Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) (90C33)

Related Items

A non-monotone inexact regularized smoothing Newton method for solving nonlinear complementarity problems, Geometric views of the generalized fischer-burmeister function and its induced merit function, An unconstrained optimization technique for large-scale linearly constrained convex minimization problems, The linear convergence of a derivative-free descent method for nonlinear complementarity problems, A wide neighborhood interior-point algorithm with arc-search for \(P_{\ast}(\kappa)\) linear complementarity problem, ON SOME NCP-FUNCTIONS BASED ON THE GENERALIZED FISCHER–BURMEISTER FUNCTION, Smoothing SQP algorithm for semismooth equations with box constraints, An \(R\)-linearly convergent derivative-free algorithm for nonlinear complementarity problems based on the generalized Fischer-Burmeister merit function, An almost smooth equation reformulation to the nonlinear complementarity problem and Newton's method, Neural network approaches based on new NCP-functions for solving tensor complementarity problem, Semismooth Newton-type method for bilevel optimization: global convergence and extensive numerical experiments, A filter method for solving nonlinear complementarity problems based on derivative-free line search, Smoothing Newton method for generalized complementarity problems based on a new smoothing function, Modified Newton methods for solving a semismooth reformulation of monotone complementarity problems, Solution of monotone complementarity problems with locally Lipschitzian functions, The semismooth-related properties of a merit function and a descent method for the nonlinear complementarity problem, On unconstrained and constrained stationary points of the implicit Lagrangian, A descent algorithm for generalized complementarity problems based on generalized Fischer-Burmeister functions, Stationary points of bound constrained minimization reformulations of complementarity problems, New NCP-functions and their properties, Global method for monotone variational inequality problems with inequality constraints, A fast algorithm for solving a class of the linear complementarity problem in a finite number of steps, A new filter method for solving nonlinear complementarity problems, Modified extragradient method for variational inequalities and verification of solution existence, Penalized NCP-functions for nonlinear complementarity problems and a scaling algorithm, A new approach to continuation methods for complementarity problems with uniform \(P\)-functions, Un algoritmo global con jacobiano suavizado para problemas de complementariedad no lineal, A feasible directions algorithm for nonlinear complementarity problems and applications in mechanics, An \((m+1)\)-step iterative method of convergence order \((m+2)\) for linear complementarity problems. An \((m+1)\)-step iterative method for LCPs, A sequential ADMM algorithm to find sparse LCP solutions using a \(l_2-l_1\) regularization technique with application in bimatrix game, A cosh-based smoothing Newton method for \(P_{0}\) nonlinear complementarity problem, Merit functions for nonsmooth complementarity problems and related descent algorithms, On solving linear complementarity problems by DC programming and DCA, Some new projection methods for variational inequalities, A smoothing inexact Newton method for \(P_0\) nonlinear complementarity problem, Predictor-corrector smoothing Newton method, based on a new smoothing function, for solving the nonlinear complementarity problem with a \(P_0\) function, The numerical study of a regularized smoothing Newton method for solving \(P_{0}\)-NCP based on the generalized smoothing Fischer-Burmeister function, A Finsler geometrical programming approach to the nonlinear complementarity problem of traffic equilibrium, A new class of penalized NCP-functions and its properties, Discovery of new complementarity functions for NCP and SOCCP, A nonmonotone derivative-free algorithm for nonlinear complementarity problems based on the new generalized penalized Fischer-Burmeister merit function, A new smoothing Broyden-like method for solving nonlinear complementarity problem with a \(P_{0}\)-function, Further application of \(H\)-differentiability to generalized complementarity problems based on generalized Fisher-Burmeister functions, Neural network for solving convex quadratic bilevel programming problems, Global convergence property of modified Levenberg-Marquardt methods for nonsmooth equations., Nonnegative inverse eigenvalue problems with partial eigendata, A regularization semismooth Newton method based on the generalized Fischer-Burmeister function for \(P_0\)-NCPs, Spectral residual methods with two new non-monotone line searches for large-scale nonlinear systems of equations, Trust-region method for box-constrained semismooth equations and its applications to complementary problems, On minimizing some merit functions for nonlinear complementarity problems under \(H\) -differentiability, A descent method for a reformulation of the second-order cone complementarity problem, An application of \(H\)-differentiability to nonnegative and unrestricted generalized complementarity problems, On a semismooth least squares formulation of complementarity problems with gap reduction, Box-constrained minimization reformulations of complementarity problems in second-order cones, A continuation method for linear complementarity problems withP₀matrix, The convergence of a one-step smoothing Newton method for \(P_0\)-NCP based on a new smoothing NCP-function, A derivative-free filter method for solving nonlinear complementarity problems, On the solution of bounded and unbounded mixed complementarity problems, An efficient algorithm for solving supply chain network equilibria and equivalent supernetwork based traffic network equilibria, Convergence analysis of nonmonotone Levenberg-Marquardt algorithms for complementarity problem, Active-set projected trust-region algorithm for box-constrained nonsmooth equations, Solving nonlinear complementarity problems with neural networks: A reformulation method approach, Nonsmooth equation based BFGS method for solving KKT systems in mathematical programming, A new smoothing and regularization Newton method for \(P_{0}\)-NCP, A neural network based on the generalized Fischer-Burmeister function for nonlinear complementarity problems, Properties of a family of merit functions and a merit function method for the NCP, A new SQP approach for nonlinear complementarity problems, Symmetrization of generalized natural residual function for NCP, Solution point characterizations and convergence analysis of a descent algorithm for nonsmooth continuous complementarity problems., A smoothing Levenberg-Marquardt method for NCP, Hybrid Newton-type method for a class of semismooth equations, A linearly convergent derivative-free descent method for the second-order cone complementarity problem, A family of NCP functions and a descent method for the nonlinear complementarity problem, Convergence analysis of nonsmooth equations for the general nonlinear complementarity problem, On minimizing and stationary sequences of a new class of merit functions for nonlinear complementarity problems, Worst-case evaluation complexity of derivative-free nonmonotone line search methods for solving nonlinear systems of equations, New constrained optimization reformulation of complementarity problems, Derivative-free methods for monotone variational inequality and complementarity problems, Properties of restricted NCP functions for nonlinear complementarity problems, Some results on the filter method for nonlinear complementary problems, Theoretical and numerical investigation of the D-gap function for box constrained variational inequalities, Convergence analysis of a trust-region multidimensional filter method for nonlinear complementarity problems, Growth behavior of a class of merit functions for the nonlinear complementarity problem, Unconstrained minimization approaches to nonlinear complementarity problems, A smoothing least square method for nonlinear complementarity problem, A new smoothing method for solving nonlinear complementarity problems, A filter method for solving nonlinear complementarity problems, A Newton-type algorithm for generalized linear complementarity problem over a polyhedral cone, Newton Hard-Thresholding Pursuit for Sparse Linear Complementarity Problem via A New Merit Function, An unconstrained smooth minimization reformulation of the second-order cone complementarity problem, A neural network for the linear complementarity problem, A partially smoothing Jacobian method for nonlinear complementarity problems with \(P_0\) function, Global Newton-type methods and semismooth reformulations for NCP, A smooth Newton method with 3-1 piecewise NCP function for generalized nonlinear complementarity problem

Uses Software

• L-BFGS
• MCPLIB

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• NE/SQP: A robust algorithm for the nonlinear complementarity problem
• A B-differentiable equation-based, globally and locally quadratically convergent algorithm for nonlinear programs, complementarity and variational inequality problems
• Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications
• Some numerical experiments with variable-storage quasi-Newton algorithms
• On the limited memory BFGS method for large scale optimization
• Über die globale Konvergenz von Variable-Metrik-Verfahren mit nicht- exakter Schrittweitenbestimmung
• Test examples for nonlinear programming codes
• Equivalent differentiable optimization problems and descent methods for asymmetric variational inequality problems
• Effiziente Schrittweitenfunktionen bei unrestringierten Optimierungsaufgaben
• Nonlinear complementarity as unconstrained and constrained minimization
• An unconstrained optimization technique for large-scale linearly constrained convex minimization problems
• On stationary points of the implicit Lagrangian for nonlinear complementarity problems
• A Newton-type method for positive-semidefinite linear complementarity problems
• Nonlinear complementarity as unconstrained optimization
• Newton's method for the nonlinear complementarity problem: a B- differentiable equation approach
• A globally convergent Newton method for solving strongly monotone variational inequalities
• Numerical Experience with Limited-Memory Quasi-Newton and Truncated Newton Methods
• Newton's Method for B-Differentiable Equations
• Updating Quasi-Newton Matrices with Limited Storage
• A Numerical Study of the Limited Memory BFGS Method and the Truncated-Newton Method for Large Scale Optimization
• Equivalence of the Complementarity Problem to a System of Nonlinear Equations
• A special newton-type optimization method
• New Error Bounds for the Linear Complementarity Problem
• Global Convergence Properties of Some Iterative Methods for Linear Complementarity Problems
• Equivalence of Complementarity Problems to Differentiable Minimization: A Unified Approach