5 research outputs found
Principled Analyses and Design of First-Order Methods with Inexact Proximal Operators
Proximal operations are among the most common primitives appearing in both
practical and theoretical (or high-level) optimization methods. This basic
operation typically consists in solving an intermediary (hopefully simpler)
optimization problem. In this work, we survey notions of inaccuracies that can
be used when solving those intermediary optimization problems. Then, we show
that worst-case guarantees for algorithms relying on such inexact proximal
operations can be systematically obtained through a generic procedure based on
semidefinite programming. This methodology is primarily based on the approach
introduced by Drori and Teboulle (Mathematical Programming, 2014) and on convex
interpolation results, and allows producing non-improvable worst-case analyzes.
In other words, for a given algorithm, the methodology generates both
worst-case certificates (i.e., proofs) and problem instances on which those
bounds are achieved.
Relying on this methodology, we provide three new methods with conceptually
simple proofs: (i) an optimized relatively inexact proximal point method, (ii)
an extension of the hybrid proximal extragradient method of Monteiro and
Svaiter (SIAM Journal on Optimization, 2013), and (iii) an inexact accelerated
forward-backward splitting supporting backtracking line-search, and both (ii)
and (iii) supporting possibly strongly convex objectives. Finally, we use the
methodology for studying a recent inexact variant of the Douglas-Rachford
splitting due to Eckstein and Yao (Mathematical Programming, 2018).
We showcase and compare the different variants of the accelerated inexact
forward-backward method on a factorization and a total variation problem.Comment: Minor modifications including acknowledgments and references. Code
available at https://github.com/mathbarre/InexactProximalOperator
International Conference on Continuous Optimization (ICCOPT) 2019 Conference Book
The Sixth International Conference on Continuous Optimization took place on the campus of the Technical University of Berlin, August 3-8, 2019. The ICCOPT is a flagship conference of the Mathematical Optimization Society (MOS), organized every three years. ICCOPT 2019 was hosted by the Weierstrass Institute for Applied Analysis and Stochastics (WIAS) Berlin. It included a Summer School and a Conference with a series of plenary and semi-plenary talks, organized and contributed sessions, and poster sessions.
This book comprises the full conference program. It contains, in particular, the scientific program in survey style as well as with all details, and information on the social program, the venue, special meetings, and more