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We prove a Perron-Frobenius-Ruelle theorem for group extensions of topological Markov chains based on a construction of $\sigma$-finite conformal measures and give applications to the construction of harmonic functions.
In this paper, a tunneling method is developed for nonlinear multiobjective optimization problems using some ideas of the single objective tunneling method. The proposed method does not require any a priori chosen parameters or ordering…
The uniqueness of the Perron vector of a nonnegative block matrix associated to a multiplex network is discussed. The conclusions come from the relationships between the irreducibility of some nonnegative block matrix associated to a…
Convergent sequences of real numbers play a fundamental role in many different problems in system theory, e.g., in Lyapunov stability analysis, as well as in optimization theory and computational game theory. In this survey, we provide an…
In this paper we analyze several new methods for solving nonconvex optimization problems with the objective function formed as a sum of two terms: one is nonconvex and smooth, and another is convex but simple and its structure is known.…
The design of fixed point algorithms is at the heart of monotone operator theory, convex analysis, and of many modern optimization problems arising in machine learning and control. This tutorial reviews recent advances in understanding the…
This paper introduces a novel approach of clustering, which is based on group consensus of dynamic linear high-order multi-agent systems. The graph topology is associated with a selected multi-agent system, with each agent corresponding to…
In this chapter we give an overview of the consensus-based global optimization algorithm and its recent variants. We recall the formulation and analytical results of the original model, then we discuss variants using component-wise…
Two finite-time consensus protocols are proposed for multi-dimensional multi-agent systems, using direction-preserving and component-wise signum controls respectively. Filippov solutions and non-smooth analysis techniques are adopted to…
The paper considers a distributed robust estimation problem over a network with directed topology involving continuous time observers. While measurements are available to the observers continuously, the nodes interact according to a…
To study the convergence to equilibrium in random maps we developed the spectral theory of the corresponding transfer (Perron-Frobenius) operators acting in a certain Banach space of generalized functions. The random maps under study in a…
Modern statistical applications often involve minimizing an objective function that may be nonsmooth and/or nonconvex. This paper focuses on a broad Bregman-surrogate algorithm framework including the local linear approximation, mirror…
We obtain non-symmetric upper and lower bounds on the rate of convergence of general monotone approximation/numerical schemes for parabolic Hamilton Jacobi Bellman Equations by introducing a new notion of consistency. We apply our general…
The paper considers a distributed robust estimation problem over a network with directed topology involving continuous time observers. While measurements are available to the observers continuously, the nodes interact according to a…
In this paper, we present monotone sequences of lower and upper bounds on the Perron value of a nonngeative matrix, and we study their strict monotonicity. Using those sequences, we provide two combinatorial applications. One is to improve…
The notion \emph{Perron-Frobenius theory} usually refers to the interaction between three properties of operator semigroups: positivity, spectrum and long-time behaviour. These interactions gives rise to a profound theory with plenty of…
Monotone systems, also known as order-preserving or cooperative systems, are prevalent in models of engineering applications such as transportation and biological networks. In this paper, we investigate the problem of finding a control…
We consider a network topology design problem in which an initial undirected graph underlying the network is given and the objective is to select a set of edges to add to the graph to optimize the coherence of the resulting network. We show…
Numerous interesting properties in nonlinear systems analysis can be written as polynomial optimization problems with nonconvex sum-of-squares problems. To solve those problems efficiently, we propose a sequential approach of local…
The problem under consideration is the synthesis of a distributed controller for a nonlinear network composed of input affine systems. The objective is to achieve exponential convergence of the solutions. To design such a feedback law,…