arXiv subjects

Demyan Yarmoshik

Publications and source records attributed to Demyan Yarmoshik.

14 recordsLinked to original sources

arXiv2026

A Communication Complexity Lower Bound for Nonuniformly Convex Consensus Optimization

We study the communication complexity of convex decentralized optimization over time-varying networks, where $n$ nodes hold private functions and must agree on the global minimizer using only synchronous exchanges with neighbors. The cost is the number of communication rounds to reach accuracy $\varepsilon$ -- a measure akin to round complexity in the LOCAL model, but constrained by nodes sharing only oracle responses. We prove a new lower bound of $Ω\!\left(χ_{\mathcal G} \sqrt{κ_g}\,\log\frac{n}{χ_{\mathcal G}}\log\frac1\varepsilon\right)$ communication rounds, where $χ_{\mathcal G}$ is the condition number of the network Laplacians and $κ_g$ that of the global objective, showing the round complexity attainable under uniform regularity cannot be matched in the nonuniform regime. The construction rests on spectral graph theory: we embed time-rotating star gadgets into the edges of an expander and patch them to preserve spectral connectivity.

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arXiv2026

Decentralized Optimization with Coupled Constraints

We consider the decentralized minimization of a separable objective $\sum_{i=1}^{n} f_i(x_i)$, where the variables are coupled through an affine constraint $\sum_{i=1}^n\left(\mathbf{A}_i x_i - b_i\right) = 0$. We assume that the functions $f_i$, matrices $\mathbf{A}_i$, and vectors $b_i$ are stored locally by the nodes of a computational network, and that the functions $f_i$ are smooth and strongly convex. This problem has significant applications in resource allocation and systems control and can also arise in distributed machine learning. We propose lower complexity bounds for decentralized optimization problems with coupled constraints and a first-order algorithm achieving the lower bounds. To the best of our knowledge, our method is also the first linearly convergent first-order decentralized algorithm for problems with general affine coupled constraints.

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arXiv2026

Decentralized Optimization with Mixed Affine Constraints

This paper considers decentralized optimization of convex functions with mixed affine equality constraints involving both local and global variables. Constraints on global variables may vary across different nodes in the network, while local variables are subject to coupled and node-specific constraints. Such problem formulations arise in machine learning applications, including federated learning and multi-task learning, as well as in resource allocation and distributed control. We analyze this problem under smooth and non-smooth assumptions, considering both strongly convex and general convex objective functions. Our main contribution is an optimal algorithm for the smooth, strongly convex regime, whose convergence rate matches established lower complexity bounds. We further provide near-optimal methods for the remaining cases.

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arXiv2025

Modeling skiers flows via Wardrope equilibrium in closed capacitated networks

We propose an equilibrium model of ski resorts where users are assigned to cycles in a closed network. As queues form on lifts with limited capacity, we derive an efficient way to find waiting times via convex optimization. The equilibrium problem is formulated as a variational inequality, and numerical experiments show that it can be solved using standard algorithms.

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arXiv2025

Stochastic Origin Frank-Wolfe for traffic assignment

In this paper, we present the Stochastic Origin Frank-Wolfe (SOFW) method, which is a special case of the block-coordinate Frank-Wolfe algorithm, applied to the problem of finding equilibrium flow distributions. By significantly reducing the computational complexity of the minimization oracle, the method improves overall efficiency at the cost of increased memory consumption. Its key advantage lies in minimizing the number of shortest path computations. We refer to existing theoretical convergence guarantees for generalized coordinate Frank-Wolfe methods and, in addition, extend the analysis by providing a convergence proof for a batched version of the Block-Coordinate Frank-Wolfe algorithm, which was not covered in the original work. We also demonstrate the practical effectiveness of our approach through experimental results. In particular, our findings show that the proposed method significantly outperforms the classical Frank-Wolfe algorithm and its variants on large-scale datasets. On smaller datasets, SOFW also remains effective, though the performance gap relative to classical methods becomes less pronounced. In such cases, there is a trade-off between solution quality, iteration time complexity, and memory usage.

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arXiv2024

An Equilibrium Dynamic Traffic Assignment Model with Linear Programming Formulation

In this paper, we consider a dynamic equilibrium transportation problem. There is a fixed number of cars moving from origin to destination areas. Preferences for arrival times are expressed as a cost of arriving before or after the preferred time at the destination. Each driver aims to minimize the time spent during the trip, making the time spent a measure of cost. The chosen routes and departure times impact the network loading. The goal is to find an equilibrium distribution across departure times and routes. For a relatively simplified transportation model we show that an equilibrium traffic distribution can be found as a solution to a linear program. In earlier works linear programming formulations were only obtained for social optimum dynamic traffic assignment problems. We also discuss algorithmic approaches for solving the equilibrium problem using time-expanded networks.

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arXiv2023

The Mirror-Prox Sliding Method for Non-smooth decentralized saddle-point problems

The saddle-point optimization problems have a lot of practical applications. This paper focuses on such non-smooth problems in decentralized case. This work contains generalization of recently proposed sliding for centralized problem. Through specific penalization method and this sliding we obtain algorithm for non-smooth decentralized saddle-point problems. Note, the proposed method approaches lower bounds both for number of communication rounds and calls of (sub-)gradient per node.

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arXiv2023

Decentralized optimization with affine constraints over time-varying networks

The decentralized optimization paradigm assumes that each term of a finite-sum objective is privately stored by the corresponding agent. Agents are only allowed to communicate with their neighbors in the communication graph. We consider the case when the agents additionally have local affine constraints and the communication graph can change over time. We provide the first linearly convergent decentralized algorithm for time-varying networks by generalizing the optimal decentralized algorithm ADOM to the case of affine constraints. We show that its rate of convergence is optimal for first-order methods by providing the lower bounds for the number of communications and oracle calls.

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arXiv2023

On accelerated coordinate descent methods for searching equilibria in two-stage transportation equilibrium traffic flow distribution model

The search for equilibrium in a two-stage traffic flow model reduces to the solution of a special nonsmooth convex optimization problem with two groups of different variables. For numerical solution of this problem, the paper proposes to use the accelerated block-coordinate Nesterov-Stich method with a special choice of block probabilities at each iteration. Theoretical estimates of the complexity of this approach can markedly improve the estimates of previously used approaches. However, in the general case they do not guarantee faster convergence. Numerical experiments with the proposed algorithms are carried out in the paper.

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arXiv2023

Primal-Dual Gradient Methods for Searching Network Equilibria in Combined Models with Nested Choice Structure and Capacity Constraints

We consider a network equilibrium model (i.e. a combined model), which was proposed as an alternative to the classic four-step approach for travel forecasting in transportation networks. This model can be formulated as a convex minimization program. We extend the combined model to the case of the stable dynamics (SD) model in the traffic assignment stage, which imposes strict capacity constraints in the network. We propose a way to solve corresponding dual optimization problems with accelerated gradient methods and give theoretical guarantees of their convergence. We conducted numerical experiments with considered optimization methods on Moscow and Berlin networks.

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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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arXiv2023

Decentralized Strongly-Convex Optimization with Affine Constraints: Primal and Dual Approaches

Decentralized optimization is a common paradigm used in distributed signal processing and sensing as well as privacy-preserving and large-scale machine learning. It is assumed that several computational entities locally hold objective functions and are connected by a network. The agents aim to commonly minimize the sum of the local objectives subject by making gradient updates and exchanging information with their immediate neighbors. Theory of decentralized optimization is pretty well-developed in the literature. In particular, it includes lower bounds and optimal algorithms. In this paper, we assume that along with an objective, each node also holds affine constraints. We discuss several primal and dual approaches to decentralized optimization problem with affine constraints.

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arXiv2022

Decentralized convex optimization under affine constraints for power systems control

Modern power systems are now in continuous process of massive changes. Increased penetration of distributed generation, usage of energy storage and controllable demand require introduction of a new control paradigm that does not rely on massive information exchange required by centralized approaches. Distributed algorithms can rely only on limited information from neighbours to obtain an optimal solution for various optimization problems, such as optimal power flow, unit commitment etc. As a generalization of these problems we consider the problem of decentralized minimization of the smooth and convex partially separable function $f = \sum_{k=1}^l f^k(x^k,\tilde x)$ under the coupled $\sum_{k=1}^l (A^k x^k - b^k) \leq 0$ and the shared $\tilde{A} \tilde{x} - \tilde{b} \leq 0$ affine constraints, where the information about $A^k$ and $b^k$ is only available for the $k$-th node of the computational network. One way to handle the coupled constraints in a distributed manner is to rewrite them in a distributed-friendly form using the Laplace matrix of the communication graph and auxiliary variables (Khamisov, CDC, 2017). Instead of using this method we reformulate the constrained optimization problem as a saddle point problem (SPP) and utilize the consensus constraint technique to make it distributed-friendly. Then we provide a complexity analysis for state-of-the-art SPP solving algorithms applied to this SPP.

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arXiv2020

Finding equilibrium in two-stage traffic assignment model

Authors describe a two-stage traffic assignment model. It contains of two blocks. The first block consists of model for calculating correspondence (demand) matrix, whereas the second block is a traffic assignment model. The first model calculates a matrix of correspondences using a matrix of transport costs. It characterizes the required volumes of movement from one area to another. The second model describes how exactly the needs for displacement, specified by the correspondence matrix, are distributed along the possible paths. It works on the basis of the Nash--Wardrop equilibrium (each driver chooses the shortest path). Knowing the ways of distribute flows along the paths, it is possible to calculate the cost matrix. Equilibrium in a two-stage model is a fixed point in the sequence of these two models. The article proposes a method of reducing the problem of finding the equilibrium to the problem of the convex non-smooth optimization. Also a numerical method for solving the obtained optimization problem is proposed. Numerical experiments were carried out for the small towns.

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