Low-rank spectral optimization via gauge duality

Abstract

Various applications in signal processing and machine learning give rise to highly structured spectral optimization problems characterized by low-rank solutions. Two important examples that motivate this work are optimization problems from phase retrieval and from blind deconvolution, which are designed to yield rank-1 solutions. An algorithm is described that is based on solving a certain constrained eigenvalue optimization problem that corresponds to the gauge dual which, unlike the more typical Lagrange dual, has an especially simple constraint. The dominant cost at each iteration is the computation of rightmost eigenpairs of a Hermitian operator. A range of numerical examples illustrate the scalability of the approach.

Final version. To appear in SIAM J. Scientific Computing

References in corpus (1)

• Self-Calibration and Biconvex Compressive Sensing

Cited by in corpus (9)

• An Optimal-Storage Approach to Semidefinite Programming using Approximate Complementarity
• Polar Alignment and Atomic Decomposition
• Maximum Regularized Likelihood Estimators: A General Prediction Theory and Applications
• Approximate methods for phase retrieval via gauge duality
• Duality of optimization problems with gauge functions
• Convex Geometry of the Generalized Matrix-Fractional Function
• Applications of gauge duality in robust principal component analysis and semidefinite programming
• Low-rank Matrix Optimization Using Polynomial-filtered Subspace Extraction
• Bundle methods for dual atomic pursuit