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 …

Minimization with orthogonality constraints (eg, X^ ⊤ X= I) and/or spherical constraints (eg,
‖ x ‖ _2= 1) has wide applications in polynomial optimization, combinatorial optimization …

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 …

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 …

Optimization problems in disciplines such as machine learning are commonly solved with
iterative methods. Gradient descent algorithms find local minima by moving along the …

In this paper we propose an efficient method for solving the spherically constrained
homogeneous polynomial optimization problem. The new approach has the following three …

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 …

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 …

This work is concerned with finding a global optimization technique for a broad class of
nonlinear optimization problems, including quadratic and polynomial optimization problems …

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 …