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The Landscape of Non-convex Quadratic Feasibility

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Citation Author(s):
Lalit Jain, Laura Balzano
Submitted by:
Amanda Bower
Last updated:
19 April 2018 - 2:10pm
Document Type:
Presentation Slides
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Presenters Name:
Amanda Bower
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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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