[图书][B] Tensor analysis: spectral theory and special tensors
L Qi, Z Luo - 2017 - SIAM
Matrix theory is one of the most fundamental tools of mathematics and science, and a
number of classical books on matrix analysis have been written to explore this theory. As a …
number of classical books on matrix analysis have been written to explore this theory. As a …
A feasible method for optimization with orthogonality constraints
Minimization with orthogonality constraints (eg, X^ ⊤ X= I) and/or spherical constraints (eg,
‖ x ‖ _2= 1) has wide applications in polynomial optimization, combinatorial optimization …
‖ x ‖ _2= 1) has wide applications in polynomial optimization, combinatorial optimization …
Most tensor problems are NP-hard
We prove that multilinear (tensor) analogues of many efficiently computable problems in
numerical linear algebra are NP-hard. Our list includes: determining the feasibility of a …
numerical linear algebra are NP-hard. Our list includes: determining the feasibility of a …
[图书][B] Global optimization: theory, algorithms, and applications
M Locatelli, F Schoen - 2013 - SIAM
The first systematic overviews on global optimization appeared in 1975–1978 thanks to two
fundamental volumes titled Towards Global Optimization (Dixon & Szegö, 1975, 1978). At …
fundamental volumes titled Towards Global Optimization (Dixon & Szegö, 1975, 1978). At …
Quantum gradient descent and Newton's method for constrained polynomial optimization
Optimization problems in disciplines such as machine learning are commonly solved with
iterative methods. Gradient descent algorithms find local minima by moving along the …
iterative methods. Gradient descent algorithms find local minima by moving along the …
Maximum block improvement and polynomial optimization
In this paper we propose an efficient method for solving the spherically constrained
homogeneous polynomial optimization problem. The new approach has the following three …
homogeneous polynomial optimization problem. The new approach has the following three …
Convex relaxation for optimal distributed control problems
This paper is concerned with the optimal distributed control (ODC) problem for linear
discrete-time deterministic and stochastic systems. The objective is to design a static …
discrete-time deterministic and stochastic systems. The objective is to design a static …
The best rank-1 approximation of a symmetric tensor and related spherical optimization problems
In this paper, we show that for a symmetric tensor, its best symmetric rank-1 approximation is
its best rank-1 approximation. Based on this result, a positive lower bound for the best rank-1 …
its best rank-1 approximation. Based on this result, a positive lower bound for the best rank-1 …
Exactness of semidefinite relaxations for nonlinear optimization problems with underlying graph structure
This work is concerned with finding a global optimization technique for a broad class of
nonlinear optimization problems, including quadratic and polynomial optimization problems …
nonlinear optimization problems, including quadratic and polynomial optimization problems …
Nonlinear Perron--Frobenius Theorems for Nonnegative Tensors
We present a unifying Perron--Frobenius theory for nonlinear spectral problems defined in
terms of nonnegative tensors. By using the concept of tensor shape partition, our results …
terms of nonnegative tensors. By using the concept of tensor shape partition, our results …