Interior-point methods for the monotone semidefinite linear complementarity problem in symmetric matrices

M Kojima, S Shindoh, S Hara - SIAM Journal on Optimization, 1997 - SIAM
The SDLCP (semidefinite linear complementarity problem) in symmetric matrices introduced
in this paper provides a unified mathematical model for various problems arising from …

Modulus-based matrix splitting methods for horizontal linear complementarity problems

F Mezzadri, E Galligani - Numerical Algorithms, 2020 - Springer
In this paper, we extend modulus-based matrix splitting iteration methods to horizontal linear
complementarity problems. We consider both standard and accelerated methods and …

The extended linear complementarity problem

OL Mangasarian, JS Pang - SIAM Journal on Matrix Analysis and Applications, 1995 - SIAM
We consider an extension of the horizontal linear complementarity problem, which we call
the extended linear complementarity problem (XLCP). With the aid of a natural bilinear …

On convergence of the modulus-based matrix splitting iteration method for horizontal linear complementarity problems of H+-matrices

H Zheng, S Vong - Applied Mathematics and Computation, 2020 - Elsevier
Horizontal linear complementarity problem has wide applications, such as in mechanical
and electrical engineering, structural mechanics, piecewise linear system …

The extended linear complementarity problem

B De Schutter, B De Moor - Mathematical Programming, 1995 - Springer
In this paper we define the Extended Linear Complementarity Problem (ELCP), an extension
of the well-known Linear Complementarity Problem (LCP). We show that the ELCP can be …

A generalization of irreducibility and diagonal dominance with applications to horizontal and vertical linear complementarity problems

F Mezzadri, E Galligani - Linear Algebra and its Applications, 2021 - Elsevier
In this paper, we generalize and analyze the concepts of diagonal dominance and
irreducibility in the framework of column and row representative matrices of a set. Our …

Splitting methods for a class of horizontal linear complementarity problems

F Mezzadri, E Galligani - Journal of Optimization Theory and Applications, 2019 - Springer
In this paper, we propose two splitting methods for solving horizontal linear complementarity
problems characterized by matrices with positive diagonal elements. The proposed …

Modulus‐based synchronous multisplitting methods for solving horizontal linear complementarity problems on parallel computers

F Mezzadri - Numerical Linear Algebra with Applications, 2020 - Wiley Online Library
In this article, we generalize modulus‐based synchronous multisplitting methods to
horizontal linear complementarity problems. In particular, first we define the methods of our …

On the extended linear complementarity problem

MS Gowda - Mathematical Programming, 1996 - Springer
For the extended linear complementarity problem (Mangasarian and Pang, 1995), we
introduce and characterize column-sufficiency, row-sufficiency and P-properties. These …

A modulus-based nonsmooth Newton's method for solving horizontal linear complementarity problems

F Mezzadri, E Galligani - Optimization Letters, 2021 - Springer
In this paper, we introduce and analyze a modulus-based nonsmooth Newton's method for
solving horizontal linear complementarity problems. In particular, we propose both a …