5 papers
Sparsity-Cone SDP Relaxations and Applications to Variable Fixing for Sparse Quadratic Programs
Di Hou, Thai P. D. Nguyen, Kim-Chuan Toh +1
Quadratic programs (QPs) with sparsity constraint are generally NP-hard, and their efficient global solution depends crucially on tractable tight convex relaxations. In this paper,…
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…
RiNNAL+: a Riemannian ALM Solver for SDP-RLT Relaxations of Mixed-Binary Quadratic Programs
Di Hou, Tianyun Tang, Kim-Chuan Toh
Doubly nonnegative (DNN) relaxation usually provides a tight lower bound for a mixed-binary quadratic program (MBQP). However, solving DNN problems is challenging because: (1) the…
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 i…