28 citations · 38 across the 17 of their papers we have counts for
13 papers · 1 filter
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…
A Semismooth Newton-Type Method for the Nearest Doubly Stochastic Matrix Problem
Hao Hu, Haesol Im, Xinxin Li +1
We study a semismooth Newton-type method for the nearest doubly stochastic matrix problem where both differentiability and nonsingularity of the Jacobian can fail. The optimality c…
A Restricted Dual Peaceman-Rachford Splitting Method for QAP
Naomi Graham, Hao Hu, Haesol Im +2
We revisit and strengthen splitting methods for solving doubly nonnegative, DNN, relaxations of the quadratic assignment problem, QAP. We use a modified restricted contractive spli…
Facial Reduction for Symmetry Reduced Semidefinite Doubly Nonnegative Programs
Hao Hu, Renata Sotirov, Henry Wolkowicz
We consider both facial reduction, \FRp, and symmetry reduction, \SRp, techniques for semidefinite programming, \SDPp. We show that the two together fit surprisingly well in an alt…
The linearization problem of a binary quadratic problem and its applications
Hao Hu, Renata Sotirov
We provide several applications of the linearization problem of a binary quadratic problem. We propose a new lower bounding strategy, called the linearization-based scheme, that is…
On Solving the Quadratic Shortest Path Problem
Hao Hu, Renata Sotirov
The quadratic shortest path problem is the problem of finding a path in a directed graph such that the sum of interaction costs over all pairs of arcs on the path is minimized. We…
Special cases of the quadratic shortest path problem
Hao Hu, Renata Sotirov
The quadratic shortest path problem (QSPP) is \textcolor{black}{the problem of finding a path with prespecified start vertex and end vertex in a digraph} such that the sum…