Tensor complementarity problems. I: Basic theory

DOI10.1007/s10957-019-01566-zzbMath1434.90203OpenAlexW2966845367MaRDI QIDQ2275267

Liqun Qi, Zheng-Hai Huang

Publication date: 2 October 2019

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

Full work available at URL: https://doi.org/10.1007/s10957-019-01566-z

zbMATH Keywords

global uniqueness and solvabilitytensor complementarity problemerror bound theorynonemptiness and compactness of the solution setstability and continuity analysis

Mathematics Subject Classification ID

Nonlinear programming (90C30) Numerical computation of solutions to systems of equations (65H10) Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) (90C33)

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Cites Work

• Unnamed Item
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• Tensor Decompositions and Applications
• Positive-definite tensors to nonlinear complementarity problems
• Higher-degree eigenvalue complementarity problems for tensors
• Eigenvalue analysis of constrained minimization problem for homogeneous polynomial
• Tensor complementarity problem and semi-positive tensors
• Global uniqueness and solvability for tensor complementarity problems
• Properties of solution set of tensor complementarity problem
• Symmetric nonnegative tensors and copositive tensors
• Strictly nonnegative tensors and nonnegative tensor partition
• The sparsest solutions to \(Z\)-tensor complementarity problems
• Generalization of an existence theorem for variational inequalities
• GUS-property for Lorentz cone linear complementarity problems on Hilbert spaces
• Copositive tensor detection and its applications in physics and hypergraphs
• Column sufficient tensors and tensor complementarity problems
• Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications
• Solvability of variational inequality problems
• Error bounds for the linear complementarity problem with a P-matrix
• An existence theorem for the complementarity problem
• Functions without exceptional family of elements and complementarity problems
• Exceptional families and existence theorems for variational inequality problems
• Exceptional family of elements for a variational inequality problem and its applications
• \(Q\)-matrices and boundedness of solutions to linear complementarity problems
• Exceptional families, topological degree and complementarity problems
• Error bounds for the solution sets of quadratic complementarity problems
• On a class of semi-positive tensors in tensor complementarity problem
• Global uniqueness and solvability of tensor variational inequalities
• \(\mathrm{P}\)-tensors, \(\mathrm{P}_0\)-tensors, and their applications
• Tensor eigenvalue complementarity problems
• Complementarity problems over a hypermatrix (tensor) set
• Copositivity detection of tensors: theory and algorithm
• Strictly semi-positive tensors and the boundedness of tensor complementarity problems
• Solution sets of quadratic complementarity problems
• Structural properties of tensors and complementarity problems
• Tensor eigenvalues and their applications
• Positive definite and Gram tensor complementarity problems
• Solution structures of tensor complementarity problem
• A class of second-order cone eigenvalue complementarity problems for higher-order tensors
• Solvability of two classes of tensor complementarity problems
• Test of copositive tensors
• Global error bounds for the tensor complementarity problem with a \(P\)-tensor
• Estimations on upper and lower bounds of solutions to a class of tensor complementarity problems
• Properties of some classes of structured tensors
• Stochastic \(R_0\) tensors to stochastic tensor complementarity problems
• On the R0-tensors and the solution map of tensor complementarity problems
• \(M\)-tensors and nonsingular \(M\)-tensors
• Eigenvalues of a real supersymmetric tensor
• Exceptionally regular tensors and tensor complementarity problems
• $M$-Tensors and Some Applications
• Polynomial complementarity problems
• A note onQ-matrices
• On the Continuity of the Solution Map in Linear Complementarity Problems
• On Solution Stability of the Linear Complementarity Problem
• On the existence and uniqueness of solutions in nonlinear complementarity theory
• Applications of Degree Theory to Linear Complementarity Problems
• The Generalized Order Linear Complementarity Problem
• Properties of Tensor Complementarity Problem and Some Classes of Structured Tensors
• A Fixed Point Iterative Method for Low $n$-Rank Tensor Pursuit
• Tensor complementarity problems: the GUS-property and an algorithm
• Properties of S-tensors
• On error bounds of polynomial complementarity problems with structured tensors
• Finite-Dimensional Variational Inequalities and Complementarity Problems
• On the properties of tensor complementarity problems
• HIGH-ORDER COPOSITIVE TENSORS AND ITS APPLICATIONS
• On $Q$-Tensors
• Tensor Analysis
• Stability of Solutions and Continuity of Solution Maps of Tensor Complementarity Problems
• Coercivity Conditions in Nonlinear Complementarity Problems
• A Partition Theorem for Euclidean n-Space
• Numerical Methods for Quasi‐Linear Elliptic Equations with Nonlinear Boundary Conditions
• On the cone eigenvalue complementarity problem for higher-order tensors

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