1 citations · 1 across the 19 of their papers we have counts for
20 papers
Convex Relaxations for the Optimization of Markov Processes
Hongyi Zhang, Yuehaw Khoo, Tianyun Tang
In this paper, we study the problem of optimizing Markov processes that interpolate between two prescribed probability distributions while minimizing a given cost. The main computa…
A preconditioned augmented Lagrangian method for solving semidefinite programming problems
Tianyun Tang, Kim-Chuan Toh
In this work, we propose a preconditioned augmented Lagrangian method (ALM) for solving semidefinite programming (SDP) problems. The preconditioner is implemented via a weighted pe…
On the efficient computation of proximal operators of affine-constrained nonconvex functions
Di Hou, Tianyun Tang, Kim-Chuan Toh +1
Proximal operators with affine constraints arise in numerous models in nonconvex projection, composite optimization, and structured regularization. However, their efficient computa…
A Low-rank Augmented Lagrangian Method for Polyhedral-SDP and Moment-SOS Relaxations of Polynomial Optimization
Di Hou, Tianyun Tang, Kim-Chuan Toh
Polynomial optimization problems (POPs) can be reformulated as geometric convex conic programs, as shown by Kim, Kojima, and Toh (SIOPT 30:1251-1273, 2020), though such formulation…
A Quadratically Convergent Alternating Projection Method for Nonconvex Sets
Nachuan Xiao, Shiwei Wang, Tianyun Tang +1
In this paper, we consider the feasibility problem, which aims to find a feasible point for the constraint set over a possibly non-regular subset…
Convex relaxation approaches for high-dimensional optimal transport
Yuehaw Khoo, Tianyun Tang
Optimal transport (OT) is a powerful tool in mathematics and data science but faces severe computational and statistical challenges in high dimensions. We propose convex relaxation…
Stiefel optimization is NP-hard
Zehua Lai, Lek-Heng Lim, Tianyun Tang
We show that linearly constrained linear optimization over a Stiefel or Grassmann manifold is NP-hard in general. We show that the same is true for unconstrained quadratic optimiza…
An Exact Penalty Approach for Equality Constrained Optimization over a Convex Set
Nachuan Xiao, Tianyun Tang, Shiwei Wang +1
In this paper, we consider the nonlinear constrained optimization problem (NCP) with constraint set , where is a closed convex subset…
A low-rank augmented Lagrangian method for doubly nonnegative relaxations of mixed-binary quadratic programs
Di Hou, Tianyun Tang, Kim-Chuan Toh
Doubly nonnegative (DNN) programming problems are known to be challenging to solve because of their huge number of constraints and variables. In this work, we int…
A Bregman ADMM for Bethe variational problem
Yuehaw Khoo, Tianyun Tang, Kim-Chuan Toh
In this work, we propose a novel Bregman ADMM with nonlinear dual update to solve the Bethe variational problem (BVP), a key optimization formulation in graphical models and statis…
Optimization over convex polyhedra via Hadamard parametrizations
Tianyun Tang, Kim-Chuan Toh
In this paper, we study linearly constrained optimization problems (LCP). After applying Hadamard parametrization, the feasible set of the parametrized problem (LCPH) becomes an al…
Exploring chordal sparsity in semidefinite programming with sparse plus low-rank data matrices
Tianyun Tang, Kim-Chuan Toh
Semidefinite programming (SDP) problems are challenging to solve because of their high dimensionality. However, solving sparse SDP problems with small tree-width are known to be re…
A feasible method for general convex low-rank SDP problems
Tianyun Tang, Kim-Chuan Toh
In this work, we consider the low rank decomposition (SDPR) of general convex semidefinite programming problems (SDP) that contain both a positive semidefinite matrix and a nonnega…
Self-adaptive ADMM for semi-strongly convex problems
Tianyun Tang, Kim-Chuan Toh
In this paper, we develop a self-adaptive ADMM that updates the penalty parameter adaptively. When one part of the objective function is strongly convex i.e., the problem is semi-s…
A Riemannian Dimension-reduced Second Order Method with Application in Sensor Network Localization
Tianyun Tang, Kim-Chuan Toh, Nachuan Xiao +1
In this paper, we propose a cubic-regularized Riemannian optimization method (RDRSOM), which partially exploits the second order information and achieves the iteration complexity o…
A feasible method for solving an SDP relaxation of the quadratic knapsack problem
Tianyun Tang, Kim-Chuan Toh
In this paper, we consider an SDP relaxation of the quadratic knapsack problem (QKP). After using the Burer-Monteiro factorization, we get a non-convex optimization problem, whose…
Accelerating nuclear-norm regularized low-rank matrix optimization through Burer-Monteiro decomposition
Ching-pei Lee, Ling Liang, Tianyun Tang +1
This work proposes a rapid algorithm, BM-Global, for nuclear-norm-regularized convex and low-rank matrix optimization problems. BM-Global efficiently decreases the objective value…
Solving graph equipartition SDPs on an algebraic variety
Tianyun Tang, Kim-Chuan Toh
Semidefinite programs are generally challenging to solve due to their high dimensionality. Burer and Monteiro developed a non-convex approach to solve linear SDP problems by applyi…
Minimizing cycles in tournaments and normalized -norms
Jie Ma, Tianyun Tang
Akin to the Erdős-Rademacher problem, Linial and Morgenstern made the following conjecture in tournaments: for any , among all -vertex tournaments with $d\binom{n}{3…
Monochromatic subgraphs in iterated triangulations
Jie Ma, Tianyun Tang, Xingxing Yu
For integers , an iterated triangulation is defined recursively as follows: is the plane triangulation on three vertices and, for , is the p…