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Alexander Gornov

Publications and source records attributed to Alexander Gornov.

9 recordsLinked to original sources
arXiv2023

Zero-Order Stochastic Conditional Gradient Sliding Method for Non-smooth Convex Optimization

The conditional gradient idea proposed by Marguerite Frank and Philip Wolfe in 1956 was so well received by the community that new algorithms (also called Frank--Wolfe type algorithms) are still being actively created. In this paper, we study a non-smooth stochastic convex optimization problem with constraints. Using a smoothing technique and based on an accelerated batched first-order Stochastic Conditional Gradient Sliding method, we propose a novel gradient-free Frank--Wolfe type algorithm called Zero-Order Stochastic Conditional Gradient Sliding (ZO-SCGS). This algorithm is robust not only for the class of non-smooth problems, but surprisingly also for the class of smooth black box problems, outperforming the SOTA algorithms in the smooth case in term oracle calls. In practical experiments we confirm our theoretical results.

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arXiv2023

A randomised non-descent method for global optimisation

This paper proposes novel algorithm for non-convex multimodal constrained optimisation problems. It is based on sequential solving restrictions of problem to sections of feasible set by random subspaces (in general, manifolds) of low dimensionality. This approach varies in a way to draw subspaces, dimensionality of subspaces, and method to solve restricted problems. We provide empirical study of algorithm on convex, unimodal and multimodal optimisation problems and compare it with efficient algorithms intended for each class of problems.

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arXiv2021

Non-convex optimization in digital pre-distortion of the signal

In this paper, we give some observation of applying modern optimization methods for functionals describing digital predistortion (DPD) of signals with orthogonal frequency division multiplexing (OFDM) modulation. The considered family of model functionals is determined by the class of cascade Wiener--Hammerstein models, which can be represented as a computational graph consisting of various nonlinear blocks. To assess optimization methods with the best convergence depth and rate as a properties of this models family we multilaterally consider modern techniques used in optimizing neural networks and numerous numerical methods used to optimize non-convex multimodal functions. The research emphasizes the most effective of the considered techniques and describes several useful observations about the model properties and optimization methods behavior.

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arXiv2020

Efficient Numerical Methods to Solve Sparse Linear Equations with Application to PageRank

In this paper, we propose three methods to solve the PageRank problem for the transition matrices with both row and column sparsity. Our methods reduce the PageRank problem to the convex optimization problem over the simplex. The first algorithm is based on the gradient descent in L1 norm instead of the Euclidean one. The second algorithm extends the Frank-Wolfe to support sparse gradient updates. The third algorithm stands for the mirror descent algorithm with a randomized projection. We proof converges rates for these methods for sparse problems as well as numerical experiments support their effectiveness.

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arXiv2019

Algorithms for local optimization of OPLS energy for large protein structures

Many problems arise in computational biology can be reduced to the minimization of energy function, that determines on the geometry of considered molecule. The solution of this problem allows in particular to solve folding and docking problems in structural biology. For the small molecules this problem is well solved. But for the large molecules ($10^4$ atoms and more) this is still an open problem. In this work we consider energy minimization problem (OPLS force field) for the large molecules but with good enough initial (starting) point. In the paper one can find a biological explanation of this assumption. Due to this assumption we reduce the global optimization problem to the local one. We compare different methods: gradient-free methods, gradient type methods (gradient method, fast gradient method, conjugate gradients (CG), LBFGS), high-order (tensor) methods. We observe that the most convenient ones in GPU realization are fast gradient descent with special line-search and CG (Polak--Ribiere--Polyak), LBFGS (memory = 3 iteration). Finally, we demonstrate how all these method work on real data set provided by BIOCAD.

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arXiv2018

A universal modification of the linear coupling method

In the late sixties, N. Shor and B. Polyak independently proposed optimal first-order methods for non-smooth convex optimization problems. In 1982 A. Nemirovski proposed optimal first-order methods for 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 convex optimization problems with intermediate smoothness. In 2013 Yu. Nesterov proposed a universal gradient method which combined all the 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 for 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 Nesterov's universal gradient method.

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arXiv2016

Efficient numerical algorithms for regularized regression problem with applications to traffic matrix estimations

In this work we collect and compare to each other many different numerical methods for regularized regression problem and for the problem of projection on a hyperplane. Such problems arise, for example, as a subproblem of demand matrix estimation in IP- networks. In this special case matrix of affine constraints has special structure: all elements are 0 or 1 and this matrix is sparse enough. We have to deal with huge-scale convex optimization problem of special type. Using the properties of the problem we try "to look inside the black-box" and to see how the best modern methods work being applied to this problem.

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