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Variational methods, new optimisation techniques and new fast numerical algorithms


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4th September 2017 to 8th September 2017
Yuri Boykov
Antonin Chambolle
Ke Chen
Thomas Pock
Christoph Schnoerr
Xue-Cheng Tai

Workshop Theme

Variational image processing typically leads to minimization problems which can be characterized by one or several of the following features: (extremely) large-scale, non-convex, non-smooth, or combinatorial. Each if these remarkable properties may be substantiated as follows: (i) The increase in the size of problem instances can be attributed to the ever increasing number of data collected by modern devices, the need to merge data from various sources (multi-modality) or the type of application (such as, e.g., video surveillance) generating vast data. (ii) Non-smoothness has been of interest to the imaging community with the inception of total variation regularization by Rudin, Osher and Fatemi in their seminal work in Physica D, 1992. Besides non-smooth regularization, non-smooth data fidelity terms have become important in order to cope, e.g., with impulse noise. But non-smoothness is also an issue in optimal parameter learning, which naturally leads to bilevel optimization problems. In cases (such as in case of total variation regularization) when the optimal solution of the lower level problem (i.e., the variational model with fixed regularization parameter) is characterized by a variational inequality, which contains the regularization parameter(s) as parameters in its own right, the overall problem falls into the realm of mathematical programs with equilibrium constraints. Such problems are non-smooth, non-convex, and they notoriously lack constraint qualification, all of which challenge stationarity principles and in particular numerical solution schemes. (iii) Non-convexity, on the other hand, is of independent interest, e.g., in image inpainting, segmentation, clustering and as a filter. An example for the latter is the l^p-quasi-norm regularization (0<p<1, instead of convex l^1-norms) in compressive sensing. (iv) Issues with combinatorial complexity when finding solutions arise in (global) minimizations in clustering, the parameter learning described above, or inpainting, to name only a few. Whenever the variational principle is originally posed in function space, then all of the aforementioned applications typically lead to highly non-linear and possibly non-smooth (systems of) partial differential equations (PDEs). On the other hand, methods based on graphs have become popular recently in image processing as they aim to guarantee (global) rather than approximate (local) solutions, possibly at the cost of non-polynomial complexity. Therefore, the aims of this workshop are to discuss recent advances in (ideally mesh independent) solvers for the associated PDE or variational inequalities, their implementation on modern computer architectures (GPU, Clusters), and the connection of these methods to solvers based on combinatorial or graph-based techniques. In particular, also the issues with fixed-point-type, first-order (gradient-based) and high-order (e.g., Newton-type) solvers and associated future directions for the community will be addressed.

Further goals of this workshop are algorithmic challenges associated with global optimization and convex relaxation methods in image processing (with a focus on compressed sensing and level set based approaches). In particular, connections between convex relaxation methods and nonsmooth/nonlinear optimization algorithms; relationships between graph theory, combinatorial and continuous optimizations; and relaxation methods for spectral and inference data models in machine learning will be addressed.

Workshop speaker list and timetable can be found in the menu on the left hand side of this overview page.

Deadline for applications: 01 June 2017

Please note members of Cambridge University are welcome to turn up and sign in as a non-registered attendee on the day(s) during the workshop and attend the lecture(s). Please note that we cannot provide you with any support including name badge, meals or accommodation.

In addition to visiting the INI, there are multiple ways in which you can participate remotely.



Registration Only
  • Registration Package: £227
  • Student Registration Package: £177

The Registration Package includes admission to all seminars, lunches and refreshments on the days that lectures take place (Monday - Friday), wine reception and formal dinner, but does not include other meals or accommodation.

Registration and Accommodation
  • Accommodation Package: £577

The Accommodation Package includes a registration fee, bed and breakfast accommodation at Churchill College from the evening of Sunday 3rd September 2017 to breakfast on Saturday 9th September 2017, together with lunches and refreshments during the days that lectures take place (Monday - Friday). The formal dinner is also included, but no other evening meals.

Formal Dinner Only
  • Formal Dinner: £50

Participants on the Accommodation Package or Registration Package, including organisers and speakers, are automatically included in this event. For all remaining participants who would like to attend the above charge will apply.


Accommodation in single study bedrooms with shared facilities, breakfast and lunches are provided at Churchill College,



Lunch will be served at Wolfson Court in the Cafeteria from 12:30 to 13:30 on days that lectures take place.

  • Accommodation Package and Registration Package participants should present their badge as payment for their meal
  • Those issued with a blue Institute door entrance card can add money onto the card via the Porters' Lodge at Wolfson Court
  • Other participants must purchase their meal using their dining card via the Porters' Lodge (forms can be found on the registration desk or at the Porters' Lodge)

Evening Meal

Participants are free to make their own arrangements for dinner.

Formal Dinner

The Formal Dinner will take place on Wednesday 6th September at Emmanuel College. Participants on the Accommodation Package or Registration Package, including organisers and speakers, are automatically included in this event.

University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons