Related papers: Universal similar triangulars method for searching…
This paper studies first order methods for solving smooth minimax optimization problems $\min_x \max_y g(x,y)$ where $g(\cdot,\cdot)$ is smooth and $g(x,\cdot)$ is concave for each $x$. In terms of $g(\cdot,y)$, we consider two settings --…
In this paper, we propose a continuous-time primal-dual approach for linearly constrained multiobjective optimization problems. A novel dynamical model, called accelerated multiobjective primal-dual flow, is presented with a second-order…
Triality theory is proved for a general unconstrained global optimization problem. The method adopted is simple but mathematically rigorous. Results show that if the primal problem and its canonical dual have the same dimension, the…
In this paper we propose a new efficient approach for numerical calculation of equillibriums in multistage transport problems. In the very core of our approach lies the proper combination of Universal Gradient Method proposed by Yu.…
We introduce a new sequential subspace optimization method for large-scale saddle-point problems. It solves iteratively a sequence of auxiliary saddle-point problems in low-dimensional subspaces, spanned by directions derived from…
This paper proposes the theoretical grounds for emulating the Dynamic System Optimum with desired arrival times on regional networks, using aggregated traffic dynamics based on the Macroscopic Fundamental Diagram. We used a projection…
Basing on some recently proposed methods for solving variational inequalities with non-smooth operators, we propose an analogue of the Mirror Prox method for the corresponding class of problems under the assumption of relative smoothness…
Mirror-prox (MP) is a well-known algorithm to solve variational inequality (VI) problems. VI with a monotone operator covers a large group of settings such as convex minimization, min-max or saddle point problems. To get a convergent…
This paper considers a general convex constrained problem setting where functions are not assumed to be differentiable nor Lipschitz continuous. Our motivation is in finding a simple first-order method for solving a wide range of convex…
Optimal transport has recently been brought forward as a tool for modeling and efficiently solving a variety of flow problems, such as origin-destination problems and multi-commodity flow problems. Although the framework has shown to be…
In this paper, a primal-dual gradient flow algorithm for distributed support vector machines (DSVM) is proposed. A network of computing nodes, each carrying a subset of horizontally partitioned large dataset is considered. The nodes are…
We introduce a primal-dual stochastic gradient oracle method for distributed convex optimization problems over networks. We show that the proposed method is optimal in terms of communication steps. Additionally, we propose a new analysis…
This paper addresses an open problem in traffic modeling: the second-order macroscopic node problem. A second-order macroscopic traffic model, in contrast to a first-order model, allows for variation of driving behavior across…
In this paper, we propose a unified procedure for calibration of macroscopic second-order multilane traffic models. The focus is on calibrating the fundamental diagram using the combination stationary detector data and GPS traces. GPS…
Uniformly regular equilibrium problems are natural generalizations of abstract equilibrium prob lems and they are defined over the uniformly prox-regular nonconvex sets. Some new efficient implicit methods for solving uniformly regular…
In this paper we study a model for traffic flow on networks based on a hyperbolic system of conservation laws with discontinuous flux. Each equation describes the density evolution of vehicles having a common path along the network. In this…
In this paper, we introduce a generalized dynamical unbalanced optimal transport framework by incorporating limited control input and mass dissipation, addressing limitations in conventional optimal transport for control applications. We…
This paper studies the distributed optimization problem when the objective functions might be nondifferentiable and subject to heterogeneous set constraints. Unlike existing subgradient methods, we focus on the case when the exact…
The Traffic Assignment Problem is a fundamental, yet computationally expensive, task in transportation modeling, especially for large-scale networks. Traditional methods require iterative simulations to reach equilibrium, making real-time…
This article devises a new numerical method for first-order transport problems by using the primal-dual weak Galerkin (PD-WG) finite element method recently developed in scientific computing. The PD-WG method is based on a variational…