Vera Roshchina

Boris Mordukhovich, Javier Peña, Vera Roshchina

We develop an approach of variational analysis and generalized differentiation to conditioning issues for two-person zero-sum matrix games. Our major results establish precise relationships between a certain condition measure of the smoothing first-order algorithm proposed by Gilpin et al. [Proceedings of the 23rd AAAI Conference (2008) pp. 75-82] and the exact bound of metric regularity for an associated set-valued mapping. In this way we compute the aforementioned condition measure in terms of the initial matrix game data.

Irenee Briquel, Felipe Cucker, Javier Pena et al.

A solution for Smale's 17th problem, for the case of systems with bounded degree was recently given. This solution, an algorithm computing approximate zeros of complex polynomial systems in average polynomial time, assumed infinite precision. In this paper we describe a finite-precision version of this algorithm. Our main result shows that this version works within the same time bounds and requires a precision which, on the average, amounts to a polynomial amount of bits in the mantissa of the intervening floating-point numbers.

Felipe Cucker, Javier Peña, Vera Roshchina

We describe and analyze an interior-point method to decide feasibility problems of second-order conic systems. A main feature of our algorithm is that arithmetic operations are performed with finite precision. Bounds for both the number of arithmetic operations and the finest precision required are exhibited.

Vinesha Peiris, Nadezda Sukhorukova, Vera Roshchina

We explore the potential for using a nonsmooth loss function based on the max-norm in the training of an artificial neural network. We hypothesise that this may lead to superior classification results in some special cases where the training data is either very small or unbalanced. Our numerical experiments performed on a simple artificial neural network with no hidden layers (a setting immediately amenable to standard nonsmooth optimisation techniques) appear to confirm our hypothesis that uniform approximation based approaches may be more suitable for the datasets with reliable training data that either is limited size or biased in terms of relative cluster sizes.