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The Landscape of Non-convex Quadratic Feasibility

Abstract: 

Motivated by applications such as ordinal embedding and collaborative ranking, we formulate homogeneous quadratic feasibility as an unconstrained, non-convex minimization problem. Our work aims to understand the landscape (local minimizers and global minimizers) of the non-convex objective, which corresponds to hinge losses arising from quadratic constraints. Under certain assumptions, we give necessary conditions for non-global, local minimizers of our objective and additionally show that in two dimensions, every local minimizer is a global minimizer. Empirically, we demonstrate that finding feasible points by solving the unconstrained optimization problem with stochastic gradient descent works reliably by utilizing large initializations.

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Paper Details

Authors:
Lalit Jain, Laura Balzano
Submitted On:
19 April 2018 - 2:10pm
Short Link:
Type:
Presentation Slides
Event:
Presenter's Name:
Amanda Bower
Paper Code:
4494
Document Year:
2018
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Document Files

ICASSP_v4.pdf

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[1] Lalit Jain, Laura Balzano, "The Landscape of Non-convex Quadratic Feasibility", IEEE SigPort, 2018. [Online]. Available: http://sigport.org/2798. Accessed: Jul. 21, 2019.
@article{2798-18,
url = {http://sigport.org/2798},
author = {Lalit Jain; Laura Balzano },
publisher = {IEEE SigPort},
title = {The Landscape of Non-convex Quadratic Feasibility},
year = {2018} }
TY - EJOUR
T1 - The Landscape of Non-convex Quadratic Feasibility
AU - Lalit Jain; Laura Balzano
PY - 2018
PB - IEEE SigPort
UR - http://sigport.org/2798
ER -
Lalit Jain, Laura Balzano. (2018). The Landscape of Non-convex Quadratic Feasibility. IEEE SigPort. http://sigport.org/2798
Lalit Jain, Laura Balzano, 2018. The Landscape of Non-convex Quadratic Feasibility. Available at: http://sigport.org/2798.
Lalit Jain, Laura Balzano. (2018). "The Landscape of Non-convex Quadratic Feasibility." Web.
1. Lalit Jain, Laura Balzano. The Landscape of Non-convex Quadratic Feasibility [Internet]. IEEE SigPort; 2018. Available from : http://sigport.org/2798