Numerical Analysis Group Internal Seminar

Please note that the list below only shows forthcoming events, which may not include regular events that have not yet been entered for the forthcoming term. Please see the past events page for a list of all seminar series that the department has on offer.

Past events in this series
24 October 2017
14:00
Abstract

One of the key challenges in revenue management is unconstraining demand data. Existing state of the art single-class unconstraining methods make restrictive assumptions about the form of the underlying demand and can perform poorly when applied to data which breaks these assumptions. In this talk, we propose a novel unconstraining method that uses Gaussian process (GP) regression. We develop a novel GP model by constructing and implementing a new non-stationary covariance function for the GP which enables it to learn and extrapolate the underlying demand trend. We show that this method can cope with important features of realistic demand data, including nonlinear demand trends, variations in total demand, lengthy periods of constraining, non-exponential inter-arrival times, and discontinuities/changepoints in demand data. In all such circumstances, our results indicate that GPs outperform existing single-class unconstraining methods.

  • Numerical Analysis Group Internal Seminar
24 October 2017
14:30
Jaroslav Fowkes
Abstract

In this talk we introduce a novel dynamic programming (DP) approximation that exploits the inherent network structure present in revenue management problems. In particular, our approximation provides a new lower bound on the value function for the DP, which enables conservative revenue forecasts to be made. Existing state of the art approximations of the revenue management DP neglect the network structure, apportioning the prices of each product, whereas our proposed method does not: we partition the network of products into clusters by apportioning the capacities of resources. Our proposed approach allows, in principle, for better approximations of the DP to be made than the decomposition methods currently implemented in industry and we see it as an important stepping stone towards better approximate DP methods in practice.

  • Numerical Analysis Group Internal Seminar
31 October 2017
14:00
Matthew Geleta
Abstract


The phenomenon of poor algorithmic scalability is a critical problem in large-scale machine learning and data science. This has led to a resurgence in the use of first-order (Hessian-free) algorithms from classical optimisation. One major drawback is that first-order methods tend to converge extremely slowly. However, there exist techniques for efficiently accelerating them.
    
The topic of this talk is the Dual Regularisation Nonlinear Acceleration algorithm (DRNA) (Geleta, 2017) for nonconvex optimisation. Numerical studies using the CUTEst optimisation problem set show the method to accelerate several nonconvex optimisation algorithms, including quasi-Newton BFGS and steepest descent methods. DRNA compares favourably with a number of existing accelerators in these studies.
    
DRNA extends to the nonconvex setting a recent acceleration algorithm due to Scieur et al. (Advances in Neural Information Processing Systems 29, 2016). We have proven theorems relating DRNA to the Kylov subspace method GMRES, as well as to Anderson's acceleration method and family of multi-secant quasi-Newton methods.
 

  • Numerical Analysis Group Internal Seminar
7 November 2017
14:00
Bartolomeo Stellato
Abstract

We develop a general purpose solver for quadratic programs based on operator splitting. We introduce a novel splitting that requires the solution of a quasi-definite linear system with the same coefficient matrix in each iteration. The resulting algorithm is very robust, and once the initial factorization is carried out, division free; it also eliminates requirements on the problem data such as positive definiteness of the objective function or linear independence of the constraint functions. Moreover, it is able to detect primal or dual infeasible problems providing infeasibility certificates. The method supports caching the factorization of the quasi-definite system and warm starting, making it efficient for solving parametrized problems arising in finance, control, and machine learning. Our open-source C implementation OSQP has a small footprint and is library-free. Numerical benchmarks on problems arising from several application domains show that OSQP is typically 10x faster than interior-point methods, especially when factorization caching or warm start is used.


This is joint work with Goran Banjac, Paul Goulart, Alberto Bemporad and Stephen Boyd
 

  • Numerical Analysis Group Internal Seminar
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