There are two approaches to adjoint algorithmic differentiation: compile
time (which includes hand written adjoints) and runtime.

Noise can have undesired effects for optimization solvers. Model-based DFO solvers naturally present some resilience to noise, further enhanced in the nAG Library.

The Numerical Algorithms Group (nAG) has collaborated with the University of Manchester on matrix function algorithms.

We took implied volatility data on a grid with 10 maturities and 40 strikes and interpolated using cubic splines. We used 10 point yield and dividend curves. This gave a total of 1,223 derivatives in (2) to compute.

We considered a Bermudan Swaption (10yr maturity, 4yr reset, semiannual
payments and exercises) driven by a one factor LIBOR Market Model (LMM).

Adjoint algorithmic differentiation (AAD) is exact up to machine precision and does not capture sensitivity to nearby non-smoothness or discontinuities. Smoothing the indicator function produces a regularization effect similar to bumping the input while maintaining the efficiency of AAD.

As part of the EU-funded Performance Optimisation and Productivity
(POP) Centre of Excellence, nAG offers HPC expertise to organisations
who want help to understand and improve the performance of
parallel software.

Nonlinear programming is one of the main tools for mathematical modelling practitioners. The applications span many industries and academic fields

Better performance is possible if independent problems are batched together.
This is often possible, e.g. XVA applications in finance. nAG has made a highly optimized GPU code allowing different sized matrices in the batch.

Convolution gridding is an important part of radio astronomy image
processing. Interferometers measure fringe visibilities of celestial objects.

As part of the EU funded Performance Optimisation and Productivity
(POP) Centre of Excellence, nAG is offering HPC expertise to organizations
who want help to understand and improve poor performance of
their parallel codes.

The Fortran code uses preconditioned GMRES to solve the Rannacher
systems. The independent tridiagonal ADI systems are all solved in
parallel. On a 12 core, dual socket machine we observe the following
performance for calibrating an SLV model on a 600   300 grid: