Everything about Linear complementarity problem

🧭 Start here: a 6-step reading path

1. Read the overview: Linear complementarity problemA 5-minute orientation
2. Skim a recent paper: A modulus-based formulation for the vertical linear complementarity problemInfluential work since 2022
3. Pick up a classic book: Finite-dimensional variational inequalities and complementarity problemsThe most-reprinted book on the subject
4. Read the landmark paper: The Linear Complementarity ProblemCited 220 times
5. Go sideways: Quadratic programmingA closely related topic
6. Go sideways: P-matrixA closely related topic

🏆 Landmark papers (most cited)

• The Linear Complementarity Problem

  B. Curtis Eaves · 1971 · Management Science · 220 citations

• A generalization of the linear complementarity problem

  Richard W. Cottle, George B. Dantzig · 1970 · Journal of Combinatorial Theory · 172 citations

• Sufficient matrices and the linear complementarity problem

  R.W. Cottle, J.-S. Pang, V. Venkateswaran · 1989 · Linear Algebra and its Applications · 119 citations

• NP-Completeness of the linear complementarity problem

  S. J. Chung · 1989 · Journal of Optimization Theory and Applications · 107 citations

• The Generalized Order Linear Complementarity Problem

  M. Seetharama Gowda, Roman Sznajder · 1994 · SIAM Journal on Matrix Analysis and Applications · 92 citations

• The Extended Linear Complementarity Problem

  O. L. Mangasarian, J. S. Pang · 1995 · SIAM Journal on Matrix Analysis and Applications · 83 citations

• Monotone solutions of the parametric linear complementarity problem

  Richard W. Cottle · 1972 · Mathematical Programming · 67 citations

• Global Optimization Approach to the Linear Complementarity Problem

  P. M. Pardalos, J. B. Rosen · 1988 · SIAM Journal on Scientific and Statistical Computing · 63 citations

🆕 Influential since 2022

• A modulus-based formulation for the vertical linear complementarity problem

  Francesco Mezzadri · 2022 · Numerical Algorithms · 37 citations

• A class of modulus-based matrix splitting methods for vertical linear complementarity problem

  Cui-Xia Li, Shi-Liang Wu · 2022 · Optimization · 16 citations

• The Perturbation Bound of the Extended Vertical Linear Complementarity Problem

  Shi-Liang Wu, Wen Li, He-Hui Wang · 2023 · Journal of the Operations Research Society of China · 13 citations

• Stochastic Approximation Methods for the Two-Stage Stochastic Linear Complementarity Problem

  Lin Chen, Yongchao Liu, Xinmin Yang · 2022 · SIAM Journal on Optimization · 12 citations

• Relaxation modulus-based matrix splitting iteration method for vertical linear complementarity problem

  Dan Wang, Jicheng Li · 2024 · Journal of Computational and Applied Mathematics · 9 citations

📚 Books worth reading

• Finite-dimensional variational inequalities and complementarity problemsFrancisco Facchinei, Jong-Shi Pang · 2003
• The linear complementarity problemRichard Cottle · 1992
• Complementarity and fixed point problemsRichard Cottle, M. L. Balinski · 1978
• Complementarity, equilibrium, efficiency, and economicsGeorge Isac, G. Isac · 2002
• 📕Linear Complementarity ProblemRichard W. Cottle, Jong-Shi Pang · 2009
• Complementarity and variational problemsMichael C. Ferris, Jong-Shi Pang · 1997
• The linear complementarity problem · 2009
• The linear complementarity problemRichard Cottle · 2009

Ranked by number of editions on Open Library, a rough measure of how lasting a book is.

🔗 Related topics

• Quadratic programming Quadratic programming (QP) is the process of solving certain mathematical optimization problems involving quadratic functions. Specifically, one seeks…
• P-matrix In mathematics, a P-matrix is a complex square matrix with every principal minor is positive. A closely related class is that of P0-matrices, which are…
• Revised simplex method In mathematical optimization, the revised simplex method is a variant of George Dantzig's simplex method for linear programming. The revised simplex method…
• Criss-cross algorithm In mathematical optimization, the criss-cross algorithm is any of a family of algorithms for linear programming. Variants of the criss-cross algorithm…
• Simplex algorithm In mathematical optimization, Dantzig's simplex algorithm (or simplex method) is an algorithm for linear programming. The name of the algorithm is derived…
• Lemke's algorithm In mathematical optimization, Lemke's algorithm is a procedure for solving linear complementarity problems, and more generally mixed linear complementarity…
• Q-matrix In mathematics, a Q-matrix is a square matrix whose associated linear complementarity problem LCP(M,q) has a solution for every vector q. M is a Q-matrix…
• Complementarity theory A complementarity problem is a type of mathematical optimization problem. It is the problem of optimizing (minimizing or maximizing) a function of two…