28 citations · 38 across the 17 of their papers we have counts for
18 papers
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…
Robust Interior Point Method for Quantum Key Distribution Rate Computation
Hao Hu, Jiyoung Im, Jie Lin +2
Security proof methods for quantum key distribution, QKD, that are based on the numerical key rate calculation problem, are powerful in principle. However, the practicality of the…
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…
Companion Surface of Danger Cylinder and its Role in Solution Variation of P3P Problem
Bo wang, Hao Hu, Caixia Zhang
Traditionally the danger cylinder is intimately related to the solution stability in P3P problem. In this work, we show that the danger cylinder is also closely related to the mult…
New insights on Multi-Solution Distribution of the P3P Problem
Bo Wang, Hao Hu, Caixia Zhang
Traditionally, the P3P problem is solved by firstly transforming its 3 quadratic equations into a quartic one, then by locating the roots of the resulting quartic equation and veri…
Geometric Interpretation of side-sharing and point-sharing solutions in the P3P Problem
Bo wang, Hao Hu, Caixia Zhang
It is well known that the P3P problem could have 1, 2, 3 and at most 4 positive solutions under different configurations among its 3 control points and the position of the optical…
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…
On the Linear Extension Complexity of Stable Set Polytopes for Perfect Graphs
Hao Hu, Monique Laurent
We study the linear extension complexity of stable set polytopes of perfect graphs. We make use of known structural results permitting to decompose perfect graphs into basic perfec…
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…