Rajni to do an internship at EPRI

Congrats Rajni for getting an internship at EPRI for the spring semester!

1 paper accepted to SICON

Our paper on delays and saturation in contact tracing for disease control [1] have been accepted to SIAM Journal of Control and Optimization!

[1] Unknown bibtex entry with key [pfpypm2021sicon]
[Bibtex]

Tianqi to do an internship at Amazon

Congrats Tianqi for getting an internship at Amazon for next summer as Applied Scientist Intern.

Rajni passes his GBO

Rajni Kant Bansal, ME Ph.D. student from our lab, passed his Graduate Board Oral Examination! Congratulations!

Pengcheng to join Peking University

Pengcheng You, a Postdoctoral researcher from our lab, will join Peking University as an Assistant Professor at College of Engineering in Spring 2022! Congratulations!

Hancheng passes his GBO

Hancheng Min, ECE Ph.D. student from our lab, passed his Graduate Board Oral Examination! Congratulations!

Agustin joins NetDLab

Agustin Castellano joins our lab as a new Ph.D. student at ECE! Welcome!

Tianqi passes his GBO

Tianqi Zheng, ECE Ph.D. student from our lab, passed his Graduate Board Oral Examination! Congratulations!

1 paper accepted to CDC 21

Our paper on tight inner approximation of the positive-semidefinite cone [1] have been accepted to IEEE Conference on Decision and Control!

[1] T. Zheng, J. Guthrie, and E. Mallada, “Inner Approximations of the Positive-Semidefinite Cone via Grassmannian Packings,” in 60th IEEE Conference on Decision and Control (CDC), 2021, pp. 981-986.

We investigate the problem of finding tight inner approximations of large dimensional positive semidefinite (PSD) cones. To solve this problem, we develop a novel decomposition framework of the PSD cone by means of conical combinations of smaller dimensional sub-cones. We show that many inner approximation techniques could be summarized within this framework, including the set of (scaled) diagonally dominant matrices, Factor-width k matrices, and Chordal Sparse matrices. Furthermore, we provide a more flexible family of inner approximations of the PSD cone, where we aim to arrange the sub-cones so that they are maximally separated from each other. In doing so, these approximations tend to occupy large fractions of the volume of the PSD cone. The proposed approach is connected to a classical packing problem in Riemannian Geometry. Precisely, we show that the problem of finding maximally distant sub-cones in an ambient PSD cone is equivalent to the problem of packing sub-spaces in a Grassmannian Manifold. We further leverage the existing computational methods for constructing packings in Grassmannian manifolds to build tighter approximations of the PSD cone. Numerical experiments show how the proposed framework can balance accuracy and computational complexity, to efficiently solve positive-semidefinite programs.

``````@inproceedings{zgm2021cdc,
abstract = {We investigate the problem of finding tight inner approximations of large dimensional positive semidefinite (PSD) cones. To solve this problem, we develop a novel decomposition framework of the PSD cone by means of conical combinations of smaller dimensional sub-cones. We show that many inner approximation techniques could be summarized within this framework, including the set of (scaled) diagonally dominant matrices, Factor-width k matrices, and Chordal Sparse matrices. Furthermore, we provide a more flexible family of inner approximations of the PSD cone, where we aim to arrange the sub-cones so that they are maximally separated from each other. In doing so, these approximations tend to occupy large fractions of the volume of the PSD cone. The proposed approach is connected to a classical packing problem in Riemannian Geometry. Precisely, we show that the problem of finding maximally distant sub-cones in an ambient PSD cone is equivalent to the problem of packing sub-spaces in a Grassmannian Manifold. We further leverage the existing computational methods for constructing packings in Grassmannian manifolds to build tighter approximations of the PSD cone. Numerical experiments show how the proposed framework can balance accuracy and computational complexity, to efficiently solve positive-semidefinite programs.},
author = {Zheng, Tianqi and Guthrie, James and Mallada, Enrique},
booktitle = {60th IEEE Conference on Decision and Control (CDC)},
doi = {10.1109/CDC45484.2021.9682923},
grants = {EPCN-1711188, CAREER-1752362, AMPS-1736448, TRIPODS-1934979},
month = {12},
pages = {981-986},
record = {presented Dec. 2022, accepted Jul. 2021, submitted Mar. 2021},
title = {Inner Approximations of the Positive-Semidefinite Cone via Grassmannian Packings},