Applications of Interior Point Methods: From Sparse Approximations to Discrete Optimal Transport

A variety of problems in modern applications of optimization require a selection of a 'sparse' solution, a vector with preferably few nonzero entries. Such problems may originate from very different applications in computational statistics, signal or image processing or compressed sensing, finance, machine learning and discrete optimal transport, to mention just a few. Sparse approximation problems are often solved with dedicated and highly specialised first-order methods of optimization. In this talk I will argue that these problems may be very efficiently solved by interior point methods. The key to their success is a design of suitable preconditioners.

The research interests of Professor Jacek Gondzio include the theory and implementation of algorithms for very large-scale optimization. He is best known for his contributions in the area of interior point methods. He was educated in Poland and since 1998 he has held a position at the School of Mathematics, the University of Edinburgh. Prof Gondzio is an Editor of four leading optimization journals: Computational Optimization and Applications, European Journal of Operational Research, Mathematical Programming Computation and Optimization Methods and Software.

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