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A comparison of solvers for linear complementarity problems arising from large-scale masonry structures

Mark Ainsworth, L. Angela Mihai (2006)

Applications of Mathematics

We compare the numerical performance of several methods for solving the discrete contact problem arising from the finite element discretisation of elastic systems with numerous contact points. The problem is formulated as a variational inequality and discretised using piecewise quadratic finite elements on a triangulation of the domain. At the discrete level, the variational inequality is reformulated as a classical linear complementarity system. We compare several state-of-art algorithms that have...

A generalized proximal point algorithm for the nonlinear complementarity problem

Regina S. Burachik, Alfredo N. Iusem (2010)

RAIRO - Operations Research

We consider a generalized proximal point method (GPPA) for solving the nonlinear complementarity problem with monotone operators in Rn. It differs from the classical proximal point method discussed by Rockafellar for the problem of finding zeroes of monotone operators in the use of generalized distances, called φ-divergences, instead of the Euclidean one. These distances play not only a regularization role but also a penalization one, forcing the sequence generated by the method to remain in the...

A modified standard embedding for linear complementarity problems

Sira Allende Allonso, Jürgen Guddat, Dieter Nowack (2004)


We propose a modified standard embedding for solving the linear complementarity problem (LCP). This embedding is a special one-parametric optimization problem P ( t ) , t [ 0 , 1 ] . Under the conditions (A3) (the Mangasarian–Fromovitz Constraint Qualification is satisfied for the feasible set M ( t ) depending on the parameter t ), (A4) ( P ( t ) is Jongen–Jonker– Twilt regular) and two technical assumptions, (A1) and (A2), there exists a path in the set of stationary points connecting the chosen starting point for P ( 0 ) with a certain...

A new non-interior continuation method for P 0 -NCP based on a SSPM-function

Liang Fang (2011)

Applications of Mathematics

In this paper, we consider a new non-interior continuation method for the solution of nonlinear complementarity problem with P 0 -function ( P 0 -NCP). The proposed algorithm is based on a smoothing symmetric perturbed minimum function (SSPM-function), and one only needs to solve one system of linear equations and to perform only one Armijo-type line search at each iteration. The method is proved to possess global and local convergence under weaker conditions. Preliminary numerical results indicate that...

A new simultaneous subgradient projection algorithm for solving a multiple-sets split feasibility problem

Yazheng Dang, Yan Gao (2014)

Applications of Mathematics

In this paper, we present a simultaneous subgradient algorithm for solving the multiple-sets split feasibility problem. The algorithm employs two extrapolated factors in each iteration, which not only improves feasibility by eliminating the need to compute the Lipschitz constant, but also enhances flexibility due to applying variable step size. The convergence of the algorithm is proved under suitable conditions. Numerical results illustrate that the new algorithm has better convergence than the...

A note on economic equilibrium with nonsatiated utility functions

Magdalena Nockowska-Rosiak (2013)

Applicationes Mathematicae

The purpose of this paper is to prove the existence of a Walrasian equilibrium for the Arrow-Debreu and Arrow-Debreu-McKenzie models with positive price vector with nonsatiated utility functions of consumers by using variational inequalities. Moreover, the same technique is used to give an alternative proof of the existence of a Walrasian equilibrium for the Arrow-Debreu and Arrow-Debreu-McKenzie models with nonnegative, nonzero price vector with nonsatiated utility functions.

A self-adaptive trust region method for the extended linear complementarity problems

Zhensheng Yu, Qiang Li (2009)

Applications of Mathematics

By using some NCP functions, we reformulate the extended linear complementarity problem as a nonsmooth equation. Then we propose a self-adaptive trust region algorithm for solving this nonsmooth equation. The novelty of this method is that the trust region radius is controlled by the objective function value which can be adjusted automatically according to the algorithm. The global convergence is obtained under mild conditions and the local superlinear convergence rate is also established under...

A semi-smooth Newton method for solving elliptic equations with gradient constraints

Roland Griesse, Karl Kunisch (2009)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Semi-smooth Newton methods for elliptic equations with gradient constraints are investigated. The one- and multi-dimensional cases are treated separately. Numerical examples illustrate the approach and as well as structural features of the solution.

A sensitivity-based extrapolation technique for the numerical solution of state-constrained optimal control problems

Michael Hintermüller, Irwin Yousept (2010)

ESAIM: Control, Optimisation and Calculus of Variations

Sensitivity analysis (with respect to the regularization parameter) of the solution of a class of regularized state constrained optimal control problems is performed. The theoretical results are then used to establish an extrapolation-based numerical scheme for solving the regularized problem for vanishing regularization parameter. In this context, the extrapolation technique provides excellent initializations along the sequence of reducing regularization parameters. Finally, the favorable numerical behavior...

A smoothing Newton method for the second-order cone complementarity problem

Jingyong Tang, Guoping He, Li Dong, Liang Fang, Jinchuan Zhou (2013)

Applications of Mathematics

In this paper we introduce a new smoothing function and show that it is coercive under suitable assumptions. Based on this new function, we propose a smoothing Newton method for solving the second-order cone complementarity problem (SOCCP). The proposed algorithm solves only one linear system of equations and performs only one line search at each iteration. It is shown that any accumulation point of the iteration sequence generated by the proposed algorithm is a solution to the SOCCP. Furthermore,...

A smoothing SAA method for a stochastic mathematical program with complementarity constraints

Jie Zhang, Li-wei Zhang, Yue Wu (2012)

Applications of Mathematics

A smoothing sample average approximation (SAA) method based on the log-exponential function is proposed for solving a stochastic mathematical program with complementarity constraints (SMPCC) considered by Birbil et al. (S. I. Birbil, G. Gürkan, O. Listes: Solving stochastic mathematical programs with complementarity constraints using simulation, Math. Oper. Res. 31 (2006), 739–760). It is demonstrated that, under suitable conditions, the optimal solution of the smoothed SAA problem converges almost...

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