相关论文: Non-convex Global Minimization and False Discovery…
The sparse spike estimation problem consists in estimating a number of off-the-grid impulsive sources from under-determined linear measurements. Information theoretic results ensure that the minimization of a non-convex functional is able…
We develop a rigorous framework for global non-convex optimization by reformulating the minimization problem as a discounted infinite-horizon optimal control problem. For non-convex, continuous, and possibly non-smooth objective functions…
Substantial progress has been made recently on developing provably accurate and efficient algorithms for low-rank matrix factorization via nonconvex optimization. While conventional wisdom often takes a dim view of nonconvex optimization…
Techniques involving factorization are found in a wide range of applications and have enjoyed significant empirical success in many fields. However, common to a vast majority of these problems is the significant disadvantage that the…
Constrained least squares regression is an essential tool for high-dimensional data analysis. Given a partition $\mathcal{G}$ of input variables, this paper considers a particular class of nonconvex constraint functions that encourage the…
This paper presents a novel convex optimization-based method for finding the globally optimal solutions of a class of mixed-integer non-convex optimal control problems. We consider problems with non-convex constraints that restrict the…
Lossless Convexification (LCvx) is a modeling approach that transforms a class of nonconvex optimal control problems, where nonconvexity primarily arises from control constraints, into convex problems through convex relaxations. These…
High-dimensional linear regression under heavy-tailed noise or outlier corruption is challenging, both computationally and statistically. Convex approaches have been proven statistically optimal but suffer from high computational costs,…
The paper provides global optimization algorithms for two particularly difficult nonconvex problems raised by hybrid system identification: switching linear regression and bounded-error estimation. While most works focus on local…
The question of fast convergence in the classical problem of high dimensional linear regression has been extensively studied. Arguably, one of the fastest procedures in practice is Iterative Hard Thresholding (IHT). Still, IHT relies…
Trace norm regularization is a widely used approach for learning low rank matrices. A standard optimization strategy is based on formulating the problem as one of low rank matrix factorization which, however, leads to a non-convex problem.…
Quadratic constrained quadratic programming problems often occur in various fields such as engineering practice, management science, and network communication. This article mainly studies a non convex quadratic programming problem with…
An algorithm for solving nonconvex smooth optimization problems is proposed, analyzed, and tested. The algorithm is an extension of the Trust Region Algorithm with Contractions and Expansions (TRACE) [Math. Prog. 162(1):132, 2017]. In…
This paper presents a general framework for generating greedy algorithms for solving convex constraint satisfaction problems for sparse solutions by mapping the satisfaction problem into one of graph traversal on a rooted tree of unknown…
This paper describes a flexible framework for generalized low-rank tensor estimation problems that includes many important instances arising from applications in computational imaging, genomics, and network analysis. The proposed estimator…
This paper presents a piecewise convexification method for solving non-convex multi-objective optimization problems with box constraints. Based on the ideas of the $\alpha$-based Branch and Bound (${\rm \alpha BB}$) method of global…
This paper considers a large class of problems where we seek to recover a low rank matrix and/or sparse vector from some set of measurements. While methods based on convex relaxations suffer from a (possibly large) estimator bias, and other…
Robust tensor recovery plays an instrumental role in robustifying tensor decompositions for multilinear data analysis against outliers, gross corruptions and missing values and has a diverse array of applications. In this paper, we study…
We present a new approach to solve the sparse approximation or best subset selection problem, namely find a $k$-sparse vector ${\bf x}\in\mathbb{R}^d$ that minimizes the $\ell_2$ residual $\lVert A{\bf x}-{\bf y} \rVert_2$. We consider a…
Non-convex optimization is a critical tool in advancing machine learning, especially for complex models like deep neural networks and support vector machines. Despite challenges such as multiple local minima and saddle points, non-convex…