Linear Complementarity Problem

By R. Cottle. Encyclopedia of Optimization, 2009

2,682 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/c5d76b44dc33bf8d4e824a7716f69ffebf907bb8

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Citations in the corpus

Properties of Tensor Complementarity Problem and Some Classes of Structured Tensors (2014, background): “nd Zhang [1] also gave the necessary and suﬃcient conditions of P-matrices. A good review of P-matrices and Q-matrices may be found in the books by Berman and Plemmons [2], and Cottle, Pang and Stone [3]. Q-matrices and P(P0)-matrices have a long history and wide applications in mathematical science”
Modulus‐based matrix splitting iteration methods for linear complementarity problems (2010, background): “For example, the Nash equilibrium point of a bimatrix game, the contact problem, and the free boundary problem for journal bearings; see [1, 2].”
Competition and Coordination in a Two‐Channel Supply Chain (2015, background): “Retailer i selects the non-negative quantity that maximizes its proﬁt: max The retailers’ equilibrium problem may be reformulated as an LCP (Adida and DeMiguel 2011): Under Assumption 1, this LCP has a unique solution (Cottle et al. 2009).”
Variational Inequalities (2009, background): “A P-Matrix is a matrix with all of its principal minors positive, see (Cottle et al., 1992 ; Murty, 1988).”
Optimal Linear Precoding Strategies for Wideband Noncooperative Systems Based on Game Theory—Part I: Nash Equilibria (2007, background): “Definition 4) and , where is intended componentwise, a sufficient condition for (71) is the following [48]:”
Convex Optimization in Signal Processing and Communications (2009, background): “, J(x) is a N-matrix [54]); iii) matrix J(x) + J(x) is positive (or negative) semidefinite, and between any pair of points x((1)) = x((2)) there is a point x such that J(x) + J(x) is positive (or negative) definite [53].”
Polynomial complementarity problems (2016, background): “Then, the local (topological) degree of Φ at the origin is called the degree of A in the LCP literature [7], [3].”
The World Gas Model: A Multi-Period Mixed Complementarity Model for the Global Natural Gas Market (2009, neutral): “Cottle et al. (1992) and Bazaraa et al. (2004) provide extensive introductions on various variants of complementarity problems.”
Linear Complementarity Formulation for Single Bottleneck Model with Heterogeneous Commuters (2010, methodology): “Furthermore, since the heterogeneous commuters model is formulated as an LCP, the equilibria can be found by Lemke’s algorithm (Cottle et al., 1992).”
An SOS1-Based Approach for Solving MPECs with a Natural Gas Market Application (2013, background): “engineering (Cottle et al. 2009).”
Policy evaluation with temporal differences: a survey and comparison (2015, methodology): “Johns et al. (2010) started from the Lasso-TD problem but reformulated it as a linear complementarity problem (Cottle et al., 1992), for which standard solvers can be employed.”