Year: 2019
Type: conference-paper
Abstract: Low-rank methods for semi-definite programming (SDP) have gained a lot of interest recently, especially in machine learning applications. Their analysis often involves determinant-based or Schatten-norm penalties, which are difficult to implement in practice due to high computational efforts. In this paper, we propose Entropy-Penalized Semi-Definite Programming (EP-SDP), which provides a unified framework for a broad class of penalty functions used in practice to promote a low-rank solution. We show that EP-SDP problems admit an efficient numerical algorithm, having (almost) linear time complexity of the gradient computation; this makes it useful for many machine learning and optimization problems. We illustrate the practical efficiency of our approach on several combinatorial optimization and machine learning problems.
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
Awards: G1017065088, G1279347439, G2776190829, Collaborative Research: TRIPODS Institute for Optimization and Learning, G4748082740, GOALI: Machine Learning Approaches for Supply Chain Decision-Making, G6410514744, G6563880843, G70659677, AF: Small: New classes of optimization methods for nonconvex large scale machine learning models., G8770029225
OpenAlex ID: W2807066077