Background: Many students in Computer Science do not have a sufficient background in applied mathematics to employ state-of-the-art optimization techniques and to judge the outcome of such techniques critically (e.g. regarding the stability/quality/accuracy of their output). At the same time, the use of optimization techniques in computer graphics is becoming ubiquitous. Treating optimization algorithms as a black box yields sub-optimal results at best. At worst, stability issues and convergence problems may prevent the solution of a problem or impede the general application of a method to a wide range of input, i.e. beyond the set of examples shown in a paper. The course will draw attention to these aspects and to current best practices. This will enable participants to judge articles that use optimization schemes critically and improve their own skill set.

Scope and Intended Audience: We aim at thoroughly covering the basic techniques in optimization, only requiring a good working knowledge of the mathematical foundations in a standard CS curriculum, in particular, multi-dimensional analysis and linear algebra. Part of the course will be suitable for a starting PhD student. On the other end, our goal is to lead up to current research including modern ideas such as compressed sensing, convex variational formulations, and sparsity-inducing norms. We aim at exposing the major underlying ideas, exposing the working principles and giving hints for a successful implementation. The course thus also caters to the experienced researcher that seeks to utilize these modern techniques. We approach these goals by discussing a mixture of classic and more modern optimization approaches. Each section is presented by an expert in the area. Further, each section is comprised of two major parts: 1.) a condensed introduction of the necessary background and 2.) its application in particular graphics problems. We aim at giving implementation hints and the exposure of current-best-practices.

Linear and Non-linear Least Squares Fitting (Granier) [pptx]
Numerical Linear Algebra (Guennebaud) [odp]
Inverse Problems (Ihrke) [pptx]
Variational Methods (Goldlücke) [pdf]
Compressive Sensing (Jacques) [pdf]

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Xavier Granier is head of the manao team at INRIA and professor at the Institut d'Optique Graduate School. His main research background is realistic rendering and global illumination. He has extended his interest from rendering to acquisition and modeling of material properties and light sources (at University of British Columbia - Vancouver - Canada), sketching interactions (with Zheijiang University - Hangzhou - China) and expressive rendering (previously called non-photorealistic rendering). Currently, the main focus of his research is the accurate simulation of optical phenomena and the creation of new technologies that combine the strengths of optics and computer graphics.

Gaël Guennebaud is a permanent researcher at Inria Bordeaux since 2008. Before that, he obtained an ERCIM fellowship to work as a post-doctoral research associate at the Computer Graphics Laboratory of ETH-Zurich with Prof. Markus Gross and at the Visual Computing Lab of CNR Pisa, working with Prof. Roberto Scopigno. He obtained a MS degree and PhD in Computer Science from the University Paul Sabatier and the Research Institute for Computer Science of Toulouse (France). His main research interest include both real-time rendering and geometry processing in general, and surface reconstruction, point-based graphics, complex appearance, and soft-shadows rendering in particular.

Ivo Ihrke is a permanent researcher at Inria Bordeaux Sud-Ouest where he leads the research group ``Generalized Image Acquisition and Analysis'' which is supported by an Emmy-Noether fellowship of the German Research Foundation (DFG). Prior to that he was heading a research group within the Cluster of Excellence ``Multimodal Computing and Interaction'' at Saarland University. He was an Associate Senior Researcher at the MPI Informatik, and associated with the Max-Planck Center for Visual Computing and Communications. Before joining Saarland University he was a postdoctoral research fellow at the University of British Columbia, Vancouver, Canada, supported by the Alexander von Humboldt-Foundation. He received a MS degree in Scientific Computing from the Royal Institute of Technology (KTH), Stockholm, Sweden (2002) and a PhD (summa cum laude) in Computer Science from Saarland University (2007). His main research interest are the modeling of forward and inverse light transport processes and computational algorithms for solving these large scale problems in the context of computational imaging, measurement, and display.

Bastian Goldlücke received a PhD on ``Multi-Camera Reconstruction and Rendering for Free-viewpoint Video'' from the MPI for computer science in Saarbruecken in 2005. Subsequently, he held PostDoc positions at the University of Bonn and TU Munich, where he worked on variational methods and convex optimization techniques, in particular for high-accuracy geometry and texture reconstruction. In 2012, he joined the Heidelberg Collaboratory for Image Processing as an assistant professor and head of the junior research group Variational Light Field Analysis. In 2013, he was awarded an ERC Starting Grant on the topic of ``Light Field Imaging and Analysis''.

Laurent Jacques received the B.Sc. in Physics, the M.Sc. in Mathematical Physics and the PhD in Mathematical Physics from the Universit{\'e} catholique de Louvain (UCL), Belgium. He was a Postdoctoral Researcher with the Communications and Remote Sensing Laboratory of UCL in 2005--2006. He obtained in Oct. 2006 a four-year (3+1) Postdoctoral funding from the Belgian FRS-FNRS in the same lab. He was a visiting Postdoctoral Researcher, in spring 2007, at Rice University (DSP/ECE, Houston, TX, USA), and from Sep. 2007 to Jul. 2009, at the Swiss Federal Institute of Technology (LTS2/EPFL, Switzerland). Formerly funded by Belgian Science Policy (Return Grant, BELSPO, 2010-2011), and as a F.R.S.-FNRS Scientific Research Worker (2011-2012) in the ICTEAM institute of UCL, he is a FNRS Research Associate since Oct. 2012. His research focuses on Sparse Representations of signals (1-D, 2-D, sphere), Compressed Sensing theory (reconstruction, quantization) and applications, Inverse Problems in general, and Computer Vision. Since 1999, Laurent Jacques has co-authored 20 papers in international journals, 38 conference proceedings and presentations in signal and image processing conferences, and three book chapters.