Journal of optimization theory and applications, ISSN 1573-2878, 2015, Volume 169, Issue 3, pp. 1069 - 1078

In this paper, we prove that a real tensor is strictly semi-positive if and only if the corresponding tensor complementarity problem has a unique solution for any nonnegative vector and that a...

Tensor complementarity | Unique solution | 34B10 | Mathematics | Theory of Computation | 15A48 | Strictly semi-positive | Strictly copositive | 47A52 | Optimization | 47H12 | 47J10 | Calculus of Variations and Optimal Control; Optimization | 47H09 | 47H07 | Applications of Mathematics | Engineering, general | Operation Research/Decision Theory | 47H15 | Information science | Analysis | Studies | Mathematical programming | Tensors | Vectors (mathematics) | Mathematical analysis | Symmetry

Tensor complementarity | Unique solution | 34B10 | Mathematics | Theory of Computation | 15A48 | Strictly semi-positive | Strictly copositive | 47A52 | Optimization | 47H12 | 47J10 | Calculus of Variations and Optimal Control; Optimization | 47H09 | 47H07 | Applications of Mathematics | Engineering, general | Operation Research/Decision Theory | 47H15 | Information science | Analysis | Studies | Mathematical programming | Tensors | Vectors (mathematics) | Mathematical analysis | Symmetry

Journal Article

Acta applicandae mathematicae, ISSN 1572-9036, 2018, Volume 162, Issue 1, pp. 165 - 183

We give an introduction to the theory and to some applications of eigenvectors of tensors...

Computational Mathematics and Numerical Analysis | 34A05, 76A15 | Liquid crystal | Calculus of Variations and Optimal Control; Optimization | 15A69, 14Q05 | Brouwer degree | Probability Theory and Stochastic Processes | Mathematics | Applications of Mathematics | Bezout theorem | Partial Differential Equations | POLYNOMIALS | EIGENVALUES | MATHEMATICS, APPLIED | OCTUPOLAR ORDER | ZEROS | Tensors | Polynomials | Eigenvectors | Subspaces | Mathematical analysis | Mathematics - Algebraic Geometry

Computational Mathematics and Numerical Analysis | 34A05, 76A15 | Liquid crystal | Calculus of Variations and Optimal Control; Optimization | 15A69, 14Q05 | Brouwer degree | Probability Theory and Stochastic Processes | Mathematics | Applications of Mathematics | Bezout theorem | Partial Differential Equations | POLYNOMIALS | EIGENVALUES | MATHEMATICS, APPLIED | OCTUPOLAR ORDER | ZEROS | Tensors | Polynomials | Eigenvectors | Subspaces | Mathematical analysis | Mathematics - Algebraic Geometry

Journal Article

2012, ISBN 9789814374682, xxii, 587

Book

Journal of optimization theory and applications, ISSN 1573-2878, 2015, Volume 168, Issue 2, pp. 475 - 487

...). For the structured tensors, such as symmetric positive-definite tensors and copositive tensors, we derive the existence theorems on a solution of these kinds of nonlinear complementarity problems...

Copositive tensor | Symmetric tensor | Mathematics | Theory of Computation | 15A69 | Optimization | 15A18 | 65F10 | Calculus of Variations and Optimal Control; Optimization | Diagonalizable tensors | Positive-definite tensor | 65F15 | Applications of Mathematics | Engineering, general | Operation Research/Decision Theory | Nonlinear complementarity problems | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Studies | Theorems | Mathematical models | Nonlinearity | Tensors | Existence theorems | Mathematical analysis | Symmetry

Copositive tensor | Symmetric tensor | Mathematics | Theory of Computation | 15A69 | Optimization | 15A18 | 65F10 | Calculus of Variations and Optimal Control; Optimization | Diagonalizable tensors | Positive-definite tensor | 65F15 | Applications of Mathematics | Engineering, general | Operation Research/Decision Theory | Nonlinear complementarity problems | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Studies | Theorems | Mathematical models | Nonlinearity | Tensors | Existence theorems | Mathematical analysis | Symmetry

Journal Article

Journal of optimization theory and applications, ISSN 1573-2878, 2014, Volume 165, Issue 3, pp. 854 - 873

In this paper, we extend some classes of structured matrices to higher-order tensors...

34B10 | Mathematics | Theory of Computation | hbox {P}_0$$ P 0 tensor | 15A48 | 47A52 | Optimization | Principal sub-tensor | 47H12 | 47J10 | P tensor | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | hbox {B}_0$$ B 0 tensor | Eigenvalues | 47H09 | 47H07 | Applications of Mathematics | Engineering, general | B tensor | 47H15 | formula presented | COMPLEMENTARITY-PROBLEMS | MATHEMATICS, APPLIED | HYPERGRAPHS | P-0 tensor | P-MATRICES | SIGNLESS LAPLACIAN TENSORS | POSITIVE DEFINITENESS | EVEN ORDER | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | H-EIGENVALUES | ERROR-BOUNDS | B-0 tensor | Studies | Matrix | Mathematical analysis | Nonlinear equations | Tensors | Structured matrices | Inequalities | Links | Nonlinearity

34B10 | Mathematics | Theory of Computation | hbox {P}_0$$ P 0 tensor | 15A48 | 47A52 | Optimization | Principal sub-tensor | 47H12 | 47J10 | P tensor | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | hbox {B}_0$$ B 0 tensor | Eigenvalues | 47H09 | 47H07 | Applications of Mathematics | Engineering, general | B tensor | 47H15 | formula presented | COMPLEMENTARITY-PROBLEMS | MATHEMATICS, APPLIED | HYPERGRAPHS | P-0 tensor | P-MATRICES | SIGNLESS LAPLACIAN TENSORS | POSITIVE DEFINITENESS | EVEN ORDER | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | H-EIGENVALUES | ERROR-BOUNDS | B-0 tensor | Studies | Matrix | Mathematical analysis | Nonlinear equations | Tensors | Structured matrices | Inequalities | Links | Nonlinearity

Journal Article

2010, New ed., ISBN 9789814313124, xiv, 363

Book

2004, 2nd ed., ISBN 0198510594, xiv, 447

Book

2015, 5th ed. 2019, Mathematical Engineering, ISBN 9783319163413, 299

This book provides a comprehensive exposition of tensor analysis. It presents modern developments in the theory of isotropic and anisotropic tensor functions...

Calculus of tensors | Continuum mechanics | Tensor algebra | Engineering | Linear and Multilinear Algebras, Matrix Theory | Differential Geometry | Continuum Mechanics and Mechanics of Materials | Classical Mechanics | Engineering mathematics

Calculus of tensors | Continuum mechanics | Tensor algebra | Engineering | Linear and Multilinear Algebras, Matrix Theory | Differential Geometry | Continuum Mechanics and Mechanics of Materials | Classical Mechanics | Engineering mathematics

eBook

Mathematical programming, ISSN 1436-4646, 2017, Volume 170, Issue 2, pp. 507 - 539

This paper studies tensor eigenvalue complementarity problems. Basic properties of standard and complementarity tensor eigenvalues are discussed...

Tensor eigenvalues | Semidefinite program | Theoretical, Mathematical and Computational Physics | Mathematics | 15A18 | Eigenvalue complementarity | Mathematical Methods in Physics | Polynomial optimization | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | 90C22 | 65K10 | 65F15 | Combinatorics | Lasserre relaxation | MATHEMATICS, APPLIED | ELASTIC-SYSTEMS | STABILITY | POLYNOMIALS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | UNILATERAL CONTACT | OPTIMIZATION | Eigenvalues | Tensors | Polynomials | Computation | Mathematical analysis | Optimization

Tensor eigenvalues | Semidefinite program | Theoretical, Mathematical and Computational Physics | Mathematics | 15A18 | Eigenvalue complementarity | Mathematical Methods in Physics | Polynomial optimization | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | 90C22 | 65K10 | 65F15 | Combinatorics | Lasserre relaxation | MATHEMATICS, APPLIED | ELASTIC-SYSTEMS | STABILITY | POLYNOMIALS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | UNILATERAL CONTACT | OPTIMIZATION | Eigenvalues | Tensors | Polynomials | Computation | Mathematical analysis | Optimization

Journal Article

Methuen's monographs on physical subjects, vii, 92 p. illus.

Book

Journal of optimization theory and applications, ISSN 1573-2878, 2017, Volume 174, Issue 3, pp. 746 - 761

A symmetric tensor is called copositive if it generates a multivariate form taking nonnegative values over the nonnegative orthant...

Symmetric tensor | Mathematics | Theory of Computation | Optimization | Strictly copositive tensor | 15A18 | 90C30 | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Positive semi-definiteness | Simplicial partition | Applications of Mathematics | Engineering, general | 65H17 | COMPLEMENTARITY-PROBLEM | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | POSITIVE-DEFINITE | Management science | Business schools | Algorithms | Analysis | Partitions | Tensors | Numerical analysis | Mathematical analysis

Symmetric tensor | Mathematics | Theory of Computation | Optimization | Strictly copositive tensor | 15A18 | 90C30 | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Positive semi-definiteness | Simplicial partition | Applications of Mathematics | Engineering, general | 65H17 | COMPLEMENTARITY-PROBLEM | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | POSITIVE-DEFINITE | Management science | Business schools | Algorithms | Analysis | Partitions | Tensors | Numerical analysis | Mathematical analysis

Journal Article

Journal of optimization theory and applications, ISSN 1573-2878, 2018, Volume 176, Issue 2, pp. 289 - 305

In this paper, one of our main purposes is to prove the boundedness of the solution set of tensor complementarity problems such that the specific bounds depend only on the structural properties of such a tensor...

Spectral radius | 34B10 | Mathematics | Theory of Computation | 15A48 | 47A52 | Optimization | Upper and lower bounds | Tensor complementarity problems | 47H12 | 47J10 | Calculus of Variations and Optimal Control; Optimization | Operator norms | Operations Research/Decision Theory | 47H09 | 47H07 | Applications of Mathematics | Engineering, general | Structured tensor | 47H15 | MATHEMATICS, APPLIED | DEFINITE | SEMI-POSITIVE TENSORS | SUPERSYMMETRIC TENSOR | EIGENVALUES | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | HIGHER-ORDER TENSORS | MATRICES | ERROR-BOUNDS | Information science | Analysis | Norms | Lower bounds | Tensors | Mathematical analysis | Upper bounds

Spectral radius | 34B10 | Mathematics | Theory of Computation | 15A48 | 47A52 | Optimization | Upper and lower bounds | Tensor complementarity problems | 47H12 | 47J10 | Calculus of Variations and Optimal Control; Optimization | Operator norms | Operations Research/Decision Theory | 47H09 | 47H07 | Applications of Mathematics | Engineering, general | Structured tensor | 47H15 | MATHEMATICS, APPLIED | DEFINITE | SEMI-POSITIVE TENSORS | SUPERSYMMETRIC TENSOR | EIGENVALUES | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | HIGHER-ORDER TENSORS | MATRICES | ERROR-BOUNDS | Information science | Analysis | Norms | Lower bounds | Tensors | Mathematical analysis | Upper bounds

Journal Article

Journal of physics. A, Mathematical and theoretical, ISSN 1751-8121, 2019, Volume 52, Issue 42, p. 425303

We provide a computer algebra package called random tensor network integrator (RTNI). It allows to compute averages of tensor networks containing multiple Haar-distributed random unitary matrices and deterministic symbolic tensors...

tensor networks | symbolic integration | random unitary matrices | PHYSICS, MULTIDISCIPLINARY | Weingarten calculus | random tensors | QUANTUM STATES | OPTIMAL CLONING | PHYSICS, MATHEMATICAL

tensor networks | symbolic integration | random unitary matrices | PHYSICS, MULTIDISCIPLINARY | Weingarten calculus | random tensors | QUANTUM STATES | OPTIMAL CLONING | PHYSICS, MATHEMATICAL

Journal Article

11/2013, ISBN 1107042194, 343

Providing a succinct yet comprehensive treatment of the essentials of modern differential geometry and topology, this book's clear prose and informal style...

Manifolds (Mathematics) | Geometry, Differential | Calculus of tensors | Forms (Mathematics) | Textbooks

Manifolds (Mathematics) | Geometry, Differential | Calculus of tensors | Forms (Mathematics) | Textbooks

eBook

INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, ISSN 0219-8878, 11/2019, Volume 16

We introduce the anisotropic tensor calculus, which is a way of handling tensors that depends on the direction remaining always in the same class...

Finsler geometry | FIELDS | Anisotropic linear connections | sprays | PHYSICS, MATHEMATICAL

Finsler geometry | FIELDS | Anisotropic linear connections | sprays | PHYSICS, MATHEMATICAL

Journal Article

2d ed., Applied mathematics series, xii, 361 p. diagrs.

Book

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