Anton Anikin

Dual approaches to the minimization of strongly convex functionals with a simple structure under affine constraints

A strongly convex function of simple structure (for example, separable) is minimized under affine constraints. A dual problem is constructed and solved by applying a fast gradient method. The necessary properties of this method are established relying on which, under rather general conditions, the solution of the primal problem can be recovered with the same accuracy as the dual solution from the sequence generated by this method in the dual space of the problem. Although this approach seems natural, some previously unpublished rather subtle results necessary for its rigorous and complete theoretical substantiation in the required generality are presented.

Evolution of mitochondrial genomes in Baikalian amphipods

BackgroundAmphipods (Crustacea) of Lake Baikal are a very numerous and diverse group of invertebrates generally believed to have originated by adaptive radiation. The evolutionary history and phylogenetic relationships in Baikalian amphipods still remain poorly understood. Sequencing of mitochondrial genomes is a relatively feasible way for obtaining a set of gene sequences suitable for robust phylogenetic inferences. The architecture of mitochondrial genomes also may provide additional information on the mechanisms of evolution of amphipods in Lake Baikal.ResultsThree complete and four nearly complete mitochondrial genomes of Baikalian amphipods were obtained by high-throughput sequencing using the Illumina platform. A phylogenetic inference based on the nucleotide sequences of all mitochondrial protein coding genes revealed the Baikalian species to be a monophyletic group relative to the nearest non-Baikalian species with a completely sequenced mitochondrial genome - Gammarus duebeni. The phylogeny of Baikalian amphipods also suggests that the shallow-water species Eulimnogammarus has likely evolved from a deep-water ancestor, however many other species have to be added to the analysis to test this hypothesis.The gene order in all mitochondrial genomes of studied Baikalian amphipods differs from the pancrustacean ground pattern. Mitochondrial genomes of four species possess 23 tRNA genes, and in three genomes the extra tRNA gene copies have likely undergone remolding. Widely varying lengths of putative control regions and other intergenic spacers are typical for the mitochondrial genomes of Baikalian amphipods.ConclusionsThe mitochondrial genomes of Baikalian amphipods display varying organization suggesting an intense rearrangement process during their evolution. Comparison of complete mitochondrial genomes is a potent approach for studying the amphipod evolution in Lake Baikal.

A universal modification of the linear coupling method

ABSTRACT In the late sixties, N. Shor and B. Polyak independently proposed optimal first-order methods for solving non-smooth convex optimization problems. In 1982 A. Nemirovski proposed optimal first-order methods for solving smooth convex optimization problems, which utilized auxiliary line search. In 1985 A. Nemirovski and Yu. Nesterov proposed a parametric family of optimal first-order methods for solving convex optimization problems with intermediate smoothness. In 2013 Yu. Nesterov proposed a universal gradient method which combined all good properties of the previous methods, except the possibility of using auxiliary line search. One can typically observe that in practice auxiliary line search improves performance for many tasks. In this paper, we propose the apparently first such method of non-smooth convex optimization allowing the use of the line search procedure. Moreover, it is based on the universal gradient method, which does not require any a priori information about the actual degree of smoothness of the problem. Numerical experiments demonstrate that the proposed method is, in some cases, considerably faster than Nesterovs universal gradient method.

A Computational Method for Solving N-Person Game

The nonzero sum n-person game has been considered. It is well known that the game can be reduced to a global optimization problem [5; 7; 14]. By extending Mills’ result [5], we derive global optimality conditions for a Nash equilibrium. In order to solve the problem numerically, we apply the Curvilinear Multistart Algorithm [2; 3] developed for finding global solutions in nonconvex optimization problems. The proposed algorithm was tested on three and four person games. Also, for the test purpose, we have considered competitions of 3 companies at the bread market of Ulaanbaatar as the three person game and solved numerically.