Description

N&O seminar: Kevin Shu (Georgia Tech)

Everyone is welcome to attend the next N&O seminar with Kevin Shu with the title 'Sparse Quadratic Programs via Polynomial Roots'.

The talk will take place online and we will watch it together in L017. For more information and registration to get the Zoom link via e-mail, please contact Willem Feijen (willem.feijen at cwi.nl), Samarth Tiwari (samarth.tiwari at cwi.nl) or Sven Polak (sven.polak at cwi.nl).

Abstract:  We'll talk about problems of optimizing a quadratic function subject to quadratic constraints, in addition to a sparsity constraint that requires that solutions have only a few nonzero entries. Such problems include sparse versions of linear regression and principal components analysis. We'll see that this problem can be formulated as a convex conical optimization problem over a sparse version of the positive semidefinite cone, and then see how we can approximate such problems using ideas arising from the study of hyperbolic polynomials. We'll also describe a fast algorithm for such problems, which performs well in practical situations.

If you would like to link to a paper, here is one: https://arxiv.org/abs/2208.11143

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• Email: Willem Feijen, Samarth Tiwari and Sven Polak
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Dutch Seminar on Optimization (online series) with Jesse van Rijn (Twente) and Sander Borst (CWI)

The Dutch Seminar on Optimization is an initiative to bring together researchers from the Netherlands and beyond, with topics that are centered around Optimization in a broad sense. We would like to invite all researchers, especially also PhD students, who are working on related topics to join the events. We hereby announce the following two talks, given by PhD-students:

Speaker: Jesse van Rijn (Twente)
Title: Towards a Lower Bound for the Average Case Runtime of Simulated Annealing on TSP
Date: Thursday 29 September, 4pm-4:30pm

Abstract:
We analyze simulated annealing (SA) for simple randomized instances of the Traveling Salesperson Problem. Our analysis shows that the theoretically optimal cooling schedule of Hajek explores members of the solution set which are in expectation far from the global optimum. We obtain a lower bound on the expected length of the final tour obtained by SA on these random instances. In addition, we also obtain an upper bound on the expected value of its variance. These bounds assume that the Markov chain that describes SA is stationary, a situation that does not truly hold in practice. Hence, we also formulate conditions under which the bounds extend to the nonstationary case. These bounds are obtained by comparing the tour length distribution to a related distribution. We furthermore provide numerical evidence for a stochastic dominance relation that appears to exist between these two distributions, and formulate a conjecture in this direction. If proved, this conjecture implies that SA stays far from the global optimum with high probability when executed for any sub-exponential number of iterations. This would show that SA requires at least exponentially many iterations to reach a global optimum with nonvanishing probability.

Speaker: Sander Borst (CWI)
Title: Selection in explorable heaps
Date: Thursday 29 September, 4:30pm-5pm

Abstract:
Explorable heap selection is the problem of selecting the nth smallest value in a binary heap, where the values can only be accessed by traversing the binary tree. In this setting we want to minimize the distance traveled in the tree. The problem is related to the node selection problem for the branch-and-bound algorithm.
The problem was originally proposed by Karp, Saks and Widgerson (FOCS '86), who also proposed algorithms for this problem. Recently we found a new algorithm, that improves on the running time. In this talk I will explain the problem, our new algorithm and the connection between the problem and branch-and-bound.

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• Email: Daniel Dadush and Sven Polak
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PhD Defence Lucas Slot (N&O)

Everyone is welcome to attend the public defense of Lucas Slot, of his thesis ' Asymptotic Analysis of Semidefinite Bounds for Polynomial Optimization and Independent Sets in Geometric Hypergraphs' .

Promotor       : Prof. Monique Laurent (CWI, Tilburg University)
Co-promotor : Prof. Etienne de Klerk (Tilburg University)

• Email: Lucas Slot
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Workshop on Solving Polynomial Equations and Applications (Semester Programme)

Polynomial equations are at the heart of many problems in pure and applied mathematics. They form a powerful tool for modelling nonlinear phenomena in the sciences. Application areas range from robotics, chemistry and computer vision to quantum physics and statistics. Recent progress has made it possible to reliably solve challenging polynomial equations arising in such practical contexts. This workshop will feature a friendly introduction to existing methods, presentations of the latest software tools and research talks by experts in the field. The focus will be on new trends and methodology, as well as applications in the sciences.

This workshop is co-organized by Monique Laurent and Simon Telen.

Here you can find more information on the program of CWI's Solving Polynomial Equations and Applications workshop.

Please register here.

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CWI Lectures on Algebraic and Geometric Methods in Optimization (2022)

How to compose a portfolio ensuring maximum revenue while minimizing risk? How to control trajectories of solutions in dynamical systems? How to find the best sphere packing or the minimum energy of an interacting particle system? How to find optimal power flows in energy networks?

Such difficult optimization problems arise in diverse fields and application areas, such as operations research, discrete geometry, machine learning, theoretical computer science, and control theory.

These CWI Lectures are devoted to novel solution methods that combine dedicated algebraic and geometric approaches and sophisticated computational tools from mathematics and computer science.

Various aspects will be covered by four world-leading experts: Amir Ali Ahmadi (Princeton University), Etienne de Klerk (Tilburg University), Rekha Thomas (University of Washington), and Frank Vallentin (Universität zu Köln).

During the event, we will celebrate Monique Laurent’s appointment as a CWI Fellow for her contributions to research in the area of Semidefinite and Polynomial Optimization. The theme of this year’s lectures was chosen in honor of Monique’s work.

The lectures are intended for a broad mathematical audience and in 2022 the program committee consists of Daniel Dadush and Guido Schäfer (Networks and Optimization Group). This event at CWI is freely accessible after registration.

Preliminary program:
13.00–13.10 Welcome
13.10–13.55 Etienne de Klerk (Tilburg University) - Proving inequalities using semidefinite programming duality: applications in the worst-case analysis of iterative methods
13.55–14.40 Frank Vallentin (Universität zu Köln) - Generalizations and Applications of the Lovász theta number
14.40–15.15 Break
15.15–16.00 Amir Ali Ahmadi (Princeton University) - Local Minima in Polynomial Optimization
16.00–16.45 Rekha Thomas (University of Washington) - Graphical Designs: Structure, Complexity and Applications
16.45–16.50 Closing
16.50–18.00 Drinks
On this page, you'll find more information about the speakers and their presentations.

For inquiries and further details about the lectures, please contact event coordinator Daniëlle Kollerie (D.C.Kollerie@cwi.nl).

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Workshop on Polynomial Optimization and Applications in Control and Energy (Semester Programme)

This workshop is devoted to the application of polynomial optimization methods in the analysis and control of dynamical systems and energy networks. The polynomial optimization approach offers a powerful framework to model hard nonconvex, nonlinear control problems as infinite dimensional linear optimization problems over measure spaces. The rich interplay between functional analysis and operator theory, and real algebraic geometry, underlies the nowadays well-known moment/sum-of-squares hierarchy of relaxations, that allows to efficiently obtain converging sequences of bounds. This approach has also been recently developed to attack large optimal power flow problems in large electrical networks. The program (under construction) will feature lectures by experts in the field and ample time will be left for discussions.

This workshop is co-organized by Monique Laurent and Bert Zwart.

Here you can find more information on the program of CWI's Polynomial Optimization and Applications in Control and Energy workshop.

Please register here.

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