alternating projection – Optimization Online

On the Cluster-aware Supervised Learning (CluSL): Frameworks, Convergent Algorithms, and Applications

Published: 2019/10/29, Updated: 2020/10/20

Data-Mining alternating projection, clustering, feature extraction, globally convergent, regularization, supervised learning

This paper proposes a cluster-aware supervised learning (CluSL) framework, which integrates the clustering analysis with supervised learning (SL). The objective of CluSL is to simultaneously find the best clusters of the data points and minimize the sum of loss functions within each cluster. This framework has many potential applications in healthcare, operations management, manufacturing, and … Read more

Local Convergence of the Heavy-ball Method and iPiano for Non-convex Optimization

Published: 2017/06/09, Updated: 2018/01/29

Peter Ochs

Nonsmooth Optimization alternating projection, averaged projection, gradient of moreau envelopes, heavy-ball method, inertial forward-backward splitting, ipiano, non-convex feasibility, prox-regularity

A local convergence result for abstract descent methods is proved. The sequence of iterates is attracted by a local (or global) minimum, stays in its neighborhood and converges within this neighborhood. This result allows algorithms to exploit local properties of the objective function. In particular, the abstract theory in this paper applies to the inertial … Read more