Work

First order algorithms for computing linear and polyhedral estimates

Year: 2024

Type: article

Abstract: It was recently shown [6, 8] that “properly built” linear and polyhedral estimates nearly attain minimax accuracy bounds in the problem of recovery of unknown signal from noisy observations of linear images of the signal when the signal set is an ellitope . However, design of nearly optimal estimates relies upon solving semidefinite optimization problems with matrix variables, what puts the synthesis of such estimates beyond the reach of the standard Interior Point algorithms of semidefinite optimization even for moderate size recovery problems. Our goal is to develop First Order Optimization algorithms for the computationally efficient design of linear and polyhedral estimates. In this paper we (a) explain how to eliminate matrix variables, thus reducing dramatically the design dimension when passing from Interior Point to First Order optimization algorithms and (b) develop and analyse a dedicated algorithm of the latter type — Composite Truncated Level method.

Source: Open Journal of Mathematical Optimization

DOI: 10.5802/ojmo.35

Authors: Yannis Bekri, Anatoli Juditsky, Arkadi Nemirovski

Institutions: Laboratoire Jean Kuntzmann, Université Grenoble Alpes, Georgia Institute of Technology

Language: English

Topic: Sparse and Compressive Sensing Techniques

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: diamond

Funder: Agence Nationale de la Recherche

Awards: MIAI @ Grenoble Alpes, G3010527862