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In this paper we prove several turnpike results for trajectories of discrete disperse dynamical systems introduced in 1980 by A. M. Rubinov, which have a prototype in mathematical economics. [ABSTRACT FROM AUTHOR]

In this paper, we study turnpike properties for discrete disperse dynamical systems generated by set-valued mappings which were introduced by A. M. Rubinov in 1980. [ABSTRACT FROM AUTHOR]

Given a convex objective function on a Banach space, which is Lipschitz on bounded sets, we consider the class of regular vector fields introduced in our previous work on descent methods. We analyze the behaviour of the values of the objective function for two iterative processes generated by a regular vector field in the presence of computational errors and show that if the computational errors tend to zero, then the values of the objective function converge to its infimum. [ABSTRACT FROM AUTHOR]

For a certain class of mean nonexpansive self-mappings of complete metric spaces, we show that all the iterates of each mapping in this class converge, uniformly on bounded subsets, to its unique fixed point. [ABSTRACT FROM AUTHOR]

Given a Lipschitz convex and coercive objective function on a Banach space, we revisit the class of regular vector fields introduced in our previous work on descent methods. Taking into account computational errors, we study the behaviour of the values of the objective function for the process generated by a regular vector field and show that if the computational errors are small enough, then the values of the objective function become close to its infimum. [ABSTRACT FROM AUTHOR]

We study the random weak ergodic property of infinite products of mappings acting on complete metric spaces. Our results describe an aspect of the asymptotic behaviour of random infinite products of such mappings. More precisely, we show that in appropriate spaces of sequences of operators there exists a subset, which is a countable intersection of open and everywhere dense sets, such that each sequence belonging to this subset has the random weak ergodic property. Then we show that several known results in the literature can be deduced from our general result. [ABSTRACT FROM AUTHOR]

In this article, we establish the existence of optimal solutions for a large class of nonconvex infinite horizon discrete-time optimal control problems. This class contains optimal control problems arising in economic dynamics which describe a model with nonconcave utility functions representing the preferences of the planner. [ABSTRACT FROM PUBLISHER]

In this work, we study the structure of optimal solutions of infinite horizon autonomous variational problems with a lower semicontinuous integrand f : Rn × Rn → R1 ∪ {∞}, where Rn is the n-dimensional Euclidean space. We also show that all the optimality notions used in the literature are equivalent for the problems with the integrand f. [ABSTRACT FROM AUTHOR]

In this article we establish nonoccurrence of gap for two classes of infinite-dimensional control systems with nonconvex integrands. For the first class of integrands we show the existence of a minimizing sequence of trajectory-control pairs with bounded controls while for the second class we establish that an infimum on the full admissible class is equal to the infimum on a set of trajectory-control pairs with controls which are bounded by the same constant. [ABSTRACT FROM AUTHOR]

In this article we study a class of minimax problems max { f ( x ), g ( x )}→ min, x ∈ R 1 where f , g ∈ C 2 ( R 1 ). We show that the subclass of all problems for which there exists a point of minimum z ∈ R 1 such that f   ( z )  =   g ( z ) and f ′( z )= g ′( z ) is small. [ABSTRACT FROM AUTHOR]

In this paper we examine the structure of extremals of variational problems with continuous integrands f: Rn × Rn → R1 which belong to a complete metric space of functions. Our results deal with the turnpike properties of variational problems. To have this property means that the solutions of the problems are determined mainly by the integrand, and are essentially independent of the choice of interval and endpoint conditions. [ABSTRACT FROM AUTHOR]