5 citations · 10 across the 7 of their papers we have counts for
7 papers
A New Complexity Metric for Nonconvex Rank-one Generalized Matrix Completion
Haixiang Zhang, Baturalp Yalcin, Javad Lavaei +1
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 qu…
Factorization Approach for Low-complexity Matrix Completion Problems: Exponential Number of Spurious Solutions and Failure of Gradient Methods
Baturalp Yalcin, Haixiang Zhang, Javad Lavaei +1
It is well-known that the Burer-Monteiro (B-M) factorization approach can efficiently solve low-rank matrix optimization problems under the RIP condition. It is natural to ask whet…
General Low-rank Matrix Optimization: Geometric Analysis and Sharper Bounds
Haixiang Zhang, Yingjie Bi, Javad Lavaei
This paper considers the global geometry of general low-rank minimization problems via the Burer-Monterio factorization approach. For the rank- case, we prove that there is no s…
Local and Global Linear Convergence of General Low-rank Matrix Recovery Problems
Yingjie Bi, Haixiang Zhang, Javad Lavaei
We study the convergence rate of gradient-based local search methods for solving low-rank matrix recovery problems with general objectives in both symmetric and asymmetric cases, u…
Stochastic Localization Methods for Convex Discrete Optimization via Simulation
Haixiang Zhang, Zeyu Zheng, Javad Lavaei
We develop and analyze a set of new sequential simulation-optimization algorithms for large-scale multi-dimensional discrete optimization via simulation problems with a convexity s…
On The Geometric Analysis of A Quartic-quadratic Optimization Problem under A Spherical Constraint
Haixiang Zhang, Andre Milzarek, Zaiwen Wen +1
This paper considers the problem of solving a special quartic-quadratic optimization problem with a single sphere constraint, namely, finding a global and local minimizer of $\frac…
An ADI Crank-Nicolson Orthogonal Spline Collocation Method for the Two-Dimensional Fractional Diffusion-Wave Equation
Graeme Fairweather, Xuehua Yang, Da Xu +1
A new method is formulated and analyzed for the approximate solution of a two-dimensional time-fractional diffusion-wave equation. In this method, orthogonal spline collocation is…