• Title invited talk:

  Low-Rank Matrix Completion (LRMC) using Nuclear Norm (NN) with Facial Reduction (FR); Applications to Robust Principal Component Analysis

  Henry Wolkowicz, University of Waterloo, Waterloo, ON, Canada. Contact: hwolkowicz@uwaterloo.ca
  Minimization of NN is often used as a convex relaxation for solving LRMC problems. This can then be solved using semidefinite programming (SDP). The SDP and its dual are regular. FR has been successful in regularizing degenerate problems. Here we take advantage of the structure at optimality for the NN minimization and show that even though strict feasibility holds, the FR framework can be successfully applied to obtain a proper face that contains the optimal set and even improves on the NN relaxation. We include numerical tests for both exact and noisy cases.

• Tutorial Session 90 minutes Title:

  - Facial Reduction in Cone Optimization with Applications to Matrix Completions

  Add to Itinerary November 5, 2018, 4:30 PM - 6:00 PM 122B, North Bldg Authors Henry Wolkowicz, University of Waterloo, Waterloo, ON, Canada. Contact: hwolkowicz@uwaterloo.ca Abstract
  Strictly feasibility is at the heart of convex optimization. This is needed for optimality conditions, stability, and algorithmic development. New optimization modelling techniques and convex relaxations for hard nonconvex problems have shown that the loss of strict feasibility is a much more pronounced phenomenon than previously realized. These new developments suggest a reappraisal. We describe the various reasons for the loss of strict feasibility, whether due to poor modelling choices or (more interestingly) rich underlying structure, and describe ways to cope with it and, in particular, "take advantage of it".