28 citations · 38 across the 17 of their papers we have counts for
7 papers · 2 filters
An Exact Dual for Second-Order Cone Programming Using Only Lorentz-Cone Constraints
Hao Hu
Without a constraint qualification, second-order cone programs can have a duality gap or an unattained dual value. For every such program with arbitrary real coefficients, we const…
Sharp Singularity-Degree Bounds for Equality-Generated SDP-RLT Relaxations of Binary Programs
Hao Hu
Singularity degree is an important measure of semidefinite programming (SDP) degeneracy, but it is generally unavailable a priori from the problem data. We augment the Shor relaxat…
Face Identification via Polyhedral Relaxations for Binary Programs: A Comparison with Factor-Width Partial Facial Reduction
Hao Hu, Blake Smith, Mingming Xu
Facial reduction (FR) is a preprocessing technique used to restore Slater's condition in semidefinite programming (SDP), but each step generally requires solving an auxiliary SDP.…
A Primal Approach to Facial Reduction for SDP Relaxations of Combinatorial Optimization Problems
Hao Hu, Mingming Xu
We propose a novel facial reduction algorithm tailored to semidefinite programming relaxations of combinatorial optimization problems with quadratic objective functions. Our method…
Face Structure in Partial Facial Reduction of Semidefinite Relaxations of Binary Programs
Hao Hu, Mingming Xu
Semidefinite relaxations of binary optimization problems often fail Slater's condition. Full facial reduction restores strict feasibility but may require auxiliary problems as cost…
On the Singularity Degree of Shor Relaxations for 0-1 Programs
Hao Hu
Shor relaxations are standard tools for nonconvex quadratic optimization, but they may fail Slater's condition. The singularity degree quantifies this degeneracy by the number of f…
SDP Approach to Quadratic Vertex-Disjoint Paths Problem
Mingming Xu, Hao Hu
We study the quadratic -vertex-disjoint paths problem (Q--VDP), which seeks vertex-disjoint paths in a directed graph that minimize a nonconvex quadratic objective functi…