arXiv subjects

Vladislav Matyukhin

Publications and source records attributed to Vladislav Matyukhin.

5 recordsLinked to original sources

arXiv2023

Sufficient conditions for multi-stages traffic assignment model to be the convex optimization problem

In this paper we consider multi-stages traffic assignment with several demand layers, user types and network types. We consider two stages: demand matrix calculation (Entropy Wilson's model) and traffic assignment models (Beckmann or Nesterov--de Palma). For the traffic assignment stage we use dual reformulation and combine these stages as a saddle-point problem (convex-concave). Then we discuss how one can solve this problem numerically.

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arXiv2021

The recovery model for the calculation of correspondence matrix for Moscow

In this paper, we consider the problem of restoring the correspondence matrix based on the observations of real correspondences in Moscow. Following the conventional approach, the transport network is considered as a directed graph whose edges correspond to road sections and the graph vertices correspond to areas that the traffic participants leave or enter. The number of city residents is considered constant. The problem of restoring the correspondence matrix is to calculate all the correspondence from the $i$ area to the $j$ area. To restore the matrix, we propose to use one of the most popular methods of calculating the correspondence matrix in urban studies -- the entropy model. In our work, we describe the evolutionary justification of the entropy model and the main idea of the transition to solving the problem of entropy-linear programming (ELP) in calculating the correspondence matrix. To solve the ELP problem, it is proposed to pass to the dual problem. In this paper, we describe several numerical optimization methods for solving this problem: the Sinkhorn method and the Accelerated Sinkhorn method. We provide numerical experiments for the following variants of cost functions: a linear cost function and a superposition of the power and logarithmic cost functions. In these functions, the cost is a combination of average time and distance between areas, which depends on the parameters. The correspondence matrix is calculated for multiple sets of parameters and then we calculate the quality of the restored matrix relative to the known correspondence matrix. We assume that the noise in the restored correspondence matrix is Gaussian, as a result, we use the standard deviation as a quality metric.

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arXiv2021

On the Computational Efficiency of Catalyst Accelerated Coordinate Descent

This article is devoted to one particular case of using universal accelerated proximal envelopes to obtain computationally efficient accelerated versions of methods used to solve various optimization problem setups. We propose a proximally accelerated coordinate descent method that achieves the efficient algorithmic complexity of iteration and allows taking advantage of the data sparseness. It was considered an example of applying the proposed approach to optimizing a SoftMax-like function, for which the described method allowing weaken the dependence of the computational complexity on the dimension $n$ in $\mathcal{O}(\sqrt{n})$ times and, in practice, demonstrates a faster convergence in comparison with standard methods. As an example of applying the proposed approach, it was shown a variant of obtaining on its basis some efficient methods for optimizing Markov Decision Processes (MDP) in a minimax formulation with a Nesterov smoothed target functional.

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arXiv2021

Adaptive Catalyst for Smooth Convex Optimization

In this paper, we present a generic framework that allows accelerating almost arbitrary non-accelerated deterministic and randomized algorithms for smooth convex optimization problems. The main approach of our envelope is the same as in Catalyst (Lin et al., 2015): an accelerated proximal outer gradient method, which is used as an envelope for a non-accelerated inner method for the $\ell_2$ regularized auxiliary problem. Our algorithm has two key differences: 1) easily verifiable stopping criteria for inner algorithm; 2) the regularization parameter can be tunned along the way. As a result, the main contribution of our work is a new framework that applies to adaptive inner algorithms: Steepest Descent, Adaptive Coordinate Descent, Alternating Minimization. Moreover, in the non-adaptive case, our approach allows obtaining Catalyst without a logarithmic factor, which appears in the standard Catalyst (Lin et al., 2015, 2018).

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arXiv2021

Accelerated Proximal Envelopes: Application to the Coordinate Descent Method

This article is devoted to one particular case of using universal accelerated proximal envelopes to obtain computationally efficient accelerated versions of methods used to solve various optimization problem setups. In this paper, we propose a proximally accelerated coordinate descent method that achieves the efficient algorithmic complexity of iteration and allows one to take advantage of the problem sparseness. An example of applying the proposed approach to optimizing a SoftMax-like function considered, for which the described method allowing weaken the dependence of the computational complexity on the dimension of the problem $n$ in $\mathcal{O}(\sqrt{n})$ times, and in practice demonstrates a faster convergence in comparison with standard methods.

math.OC↗