VA & Opt Webinar: Javier Peña

Title: The condition number of a function relative to a set

Speaker: Javier Peña (Carnegie-Mellon University)

Date and Time: March 3rd, 2021, 11:00 AEDT (Register here for remote connection via Zoom)

Abstract: The condition number of a differentiable convex function, namely the ratio of its smoothness to strong convexity constants, is closely tied to fundamental properties of the function. In particular, the condition number of a quadratic convex function is the square of the aspect ratio of a canonical ellipsoid associated to the function. Furthermore, the condition number of a function bounds the linear rate of convergence of the gradient descent algorithm for unconstrained convex minimization.

We propose a condition number of a differentiable convex function relative to a reference set and distance function pair. This relative condition number is defined as the ratio of a relative smoothness to a relative strong convexity constants. We show that the relative condition number extends the main properties of the traditional condition number both in terms of its geometric insight and in terms of its role in characterizing the linear convergence of first-order methods for constrained convex minimization.

This is joint work with David H. Gutman at Texas Tech University.

VA & Opt Webinar: Nguyen Duy Cuong

Title: Necessary conditions for transversality properties

Speaker: Nguyen Duy Cuong (Federation University)

Date and Time: February 24th, 2021, 17:00 AEDT (Register here for remote connection via Zoom)

Abstract: Transversality properties of collections of sets play an important role in optimization and variational analysis, e.g., as constraint qualifications, qualification conditions in subdifferential, normal cone and coderivative calculus, and convergence analysis of computational algorithms. In this talk, we present some new results on primal (geometric, metric, slope) and dual (subdifferential, normal cone) necessary (in some cases also sufficient) conditions for transversality properties in both linear and nonlinear settings. Quantitative relations between transversality properties and the corresponding regularity properties of set-valued mappings are also discussed.

VA & Opt Webinar: Alexander J. Zaslavski

Title: Subgradient Projection Algorithm with Computational Errors

Speaker: Alexander J. Zaslavski (The Technion – Israel Institute of Technology)

Date and Time: February 17th, 2021, 17:00 AEDT (Register here for remote connection via Zoom)

Abstract: We study the subgradient projection algorithm for minimization of convex and nonsmooth functions, under the presence of computational errors. We show that our algorithms generate a good approximate solution, if computational errors are bounded from above by a small positive constant. Moreover, for a known computational error, we find out what an approximate solution can be obtained and how many iterates one needs for this.

Positions Available at UNSW: Applied Maths, Pure Maths & Data Science


Five positions are currently available in the School of Mathematics and Statistics. Please see the position descriptions below, for:

Please apply for these positions via Jobs@UNSW

For more information, please refer to:

https://www.maths.unsw.edu.au/news/2021-02/positions-available

Master’s program in Economic Analysis IDEA, at the Universidad Autònoma de Barcelona

Master’s program in Economic Analysis IDEA, at the Universidad Autònoma de Barcelona is available for the 2021-2022 academic year of scholarships from the Severo Ochoa program to fund the most outstanding applicants.

The IDEA master is a two-year program with a genuinely international vocation and committed to rigorous and quality training. The program is taught entirely in English.

The graduates of the program are highly appreciated in the labor market, both in national and international markets, and a significant number of them continue their training in our Doctorate in Economic Analysis as well as in prestigious national and international doctoral programs.

Complete information about our program is available on the Master’s degree website http://idea.uab.es/ .

VA & Opt Webinar: Nam Ho-Nguyen

Title: Coordinate Descent Without Coordinates: Tangent Subspace Descent on Riemannian Manifolds

Speaker: Nam Ho-Nguyen (University of Sydney)

Date and Time: February 10th, 2021, 11:00 AEDT (Register here for remote connection via Zoom)

Abstract: We consider an extension of the coordinate descent algorithm to manifold domains, and provide convergence analyses for geodesically convex and non-convex smooth objective functions. Our key insight is to draw an analogy between coordinate blocks in Euclidean space and tangent subspaces of a manifold. Hence, our method is called tangent subspace descent (TSD). The core principle behind ensuring convergence of TSD is the appropriate choice of subspace at each iteration. To this end, we propose two novel conditions: the gap ensuring and C-randomized norm conditions on deterministic and randomized modes of subspace selection respectively. These ensure convergence for smooth functions, and are satisfied in practical contexts. We propose two subspace selection rules of particular practical interest that satisfy these conditions: a deterministic one for the manifold of square orthogonal matrices, and a randomized one for the more general Stiefel manifold. (This is joint work with David Huckleberry Gutman, Texas Tech University.)

International Conference “DYNAMICAL SYSTEMS: STABILITY, CONTROL, OPTIMIZATION” (DSSCO’21) in memory of Professor R.F. Gabasov (October 5-10, 2021, Minsk)

December 17, 2020 marks the 85th anniversary of the birth of Rafail Fedorovich Gabasov, Professor, Doctor of Sciences, Honored scientist of the Republic of Belarus, world-renowned researcher in the field of optimization and optimal control (1935-2020).
R.F. Gabasov was one of the founders of the Faculty of Applied Mathematics (now the Faculty of Applied Mathematics and Computer Science) of the Belarusian State University and the Chair of Optimal Control Methods Department for many years (1967-2000). In 2000-2018 he was a professor of that department.
In memory of Rafail Fedorovich Gabasov Belarusian State University and the Institute of Mathematics of the National Academy of Sciences of Belarus are organizing the International Conference “Dynamical Systems: Stability, Control, Optimization” (DSSCO’21).
The conference will be held on October 5-10, 2021 in Minsk, Belarus, at the Belarusian State University.

For more information, please refer to

Web-page: http://conf.bsu.by/dssco_eng
Email: mou.fpmi@gmail.com
Secretary:
Vital Alsevich, tel.: +375(17)209-50-74, email: alsevichvv@mail.ru