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In this paper, we study a distributed optimization problem for a class of high-order multi-agent systems with unknown dynamics. In comparison with existing results for integrators or linear agents, we need to overcome the difficulties…
We present a novel particle filtering framework for continuous-time dynamical systems with continuous-time measurements. Our approach is based on the duality between estimation and optimal control, which allows reformulating the estimation…
We propose novel parameter estimation algorithms for a class of dynamical systems with nonlinear parametrization. The class is initially restricted to smooth monotonic functions with respect to a linear functional of the parameters. We show…
Machine learning algorithms have been used widely in various applications and areas. To fit a machine learning model into different problems, its hyper-parameters must be tuned. Selecting the best hyper-parameter configuration for machine…
Various versions of the Dynamical Systems Method (DSM) are proposed for solving linear ill-posed problems with bounded and unbounded operators. Convergence of the proposed methods is proved. Some new results concerning discrepancy principle…
Solving nonlinear SMT problems over real numbers has wide applications in robotics and AI. While significant progress is made in solving quantifier-free SMT formulas in the domain, quantified formulas have been much less investigated. We…
Sampling-based motion planning algorithms have been continuously developed for more than two decades. Apart from mobile robots, they are also widely used in manipulator motion planning. Hence, these methods play a key role in collaborative…
We establish new results of first-order necessary conditions of optimality for finite-dimensional problems with inequality constraints and for problems with equality and inequality constraints, in the form of John's theorem and in the form…
Discretizations of infinite-dimensional variational inequalities lead to linear and nonlinear complementarity problems with many degrees of freedom. To solve these problems in a parallel computing environment, we propose two active-set…
The intrinsic energy minimization in dynamical systems offers a valuable tool for minimizing the objective functions of computationally challenging problems in combinatorial optimization. However, most prior works have focused on mapping…
In this paper, we address the identification problem for the systems characterized by linear time-invariant dynamics with bilinear observation models. More precisely, we consider a suitable parametric description of the system and formulate…
In this paper we study the regularity properties of fractional maximal operators acting on $BV$-functions. We establish new bounds for the derivative of the fractional maximal function, both in the continuous and in the discrete settings.
In this paper we present novel algorithmic solutions for several resource processing and data transfer multicriteria optimization problems. The results of most of the presented techniques are strategies which solve the considered problems…
The Maximum Balanced Biclique Problem (MBBP) is a prominent model with numerous applications. Yet, the problem is NP-hard and thus computationally challenging. We propose novel ideas for designing effective exact algorithms for MBBP.…
Berge's maximum theorem gives conditions ensuring the continuity of an optimised function as a parameter changes. In this paper we state and prove the maximum theorem in terms of the theory of monoidal topology and the theory of double…
In this paper, we derive sufficient and necessary maximum principles for a stochastic optimal control problem where the system state is given by a controlled stochastic differential equation with default. We prove existence of a unique…
The maximum principle for SPDEs is established in multidimensional $C^{1}$ domains. An application is given to proving the H\"older continuity up to the boundary of solutions of one-dimensional SPDEs.
We propose a neural network approach to model general interaction dynamics and an adjoint based stochastic gradient descent algorithm to calibrate its parameters. The parameter calibration problem is considered as optimal control problem…
A refined version of the strong maximum principle is proven for a class of second order ordinary differential equations with possibly discontinuous non-monotone nonlinearities. Then, exploiting this tool, some optimal regularity results…
We introduce a novel kind of robustness in linear programming. A solution x* is called robust optimal if for all realizations of objective functions coefficients and constraint matrix entries from given interval domains there are…