We study a general matrix optimization problem with a fixed-rank positive semidefinite (PSD)
constraint. We perform the Burer-Monteiro factorization and consider a particular …

Many fundamental low-rank optimization problems, such as matrix completion, phase
retrieval, and robust PCA, can be formulated as the matrix sensing problem. Two main …

Optimal control problems can be solved via a one-shot (single) optimization or a sequence
of optimization using dynamic programming (DP). However, the computation of their global …

The problem of approximating a dense matrix by a product of sparse factors is a
fundamental problem for many signal processing and machine learning tasks. It can be …

In this work, we develop a new complexity metric for an important class of low-rank matrix
optimization problems in both symmetric and asymmetric cases, where the metric aims to …

Convergence guarantees for optimization over bounded-rank matrices are delicate to obtain
because the feasible set is a non-smooth and non-convex algebraic variety. Existing …

In this paper, we aim at computing all local minimizers of a polynomial optimization problem
under genericity conditions. By using a technique in symbolic computation, we provide a …

We describe a line-search algorithm which achieves the best-known worst-case complexity
results for problems with a certain" strict saddle" property that has been observed to hold in …

In this work, we develop a new complexity metric for an important class of low-rank matrix
optimization problems, where the metric aims to quantify the complexity of the nonconvex …

Matrix completion, a crucial sub-problem of non-convex matrix sensing, is integral to
numerous machine learning applications such as recommender systems. Traditionally …