Related papers: Analogue of Pontryagin's maximum principle for mul…
In this article we derive a Pontryagin maximum principle (PMP) for discrete-time optimal control problems on matrix Lie groups. The PMP provides first order necessary conditions for optimality; these necessary conditions typically yield two…
In this paper the necessary conditions of optimality in the form of maximum principle are derived for a very general class of variational problems. This class includes problems with any optimization criteria and constraints that can be…
This article makes no claim to originality, other than, perhaps, the simple statement here called the {\it Abstract Maximum Principle}. Actually, the whole contents are strongly based on some H. Sussmann's and coauthors' papers, in which,…
The paper concerns the study of the Pontryagin Maximum Principle for an infinite dimensional and infinite horizon boundary control problem for linear partial differential equations. The optimal control model has already been studied both in…
We establish a Pontryagin maximum principle for discrete time optimal control problems under the following three types of constraints: a) constraints on the states pointwise in time, b) constraints on the control actions pointwise in time,…
We study a constrained optimal control problem for an ensemble of control systems. Each sub-system (or plant) evolves on a matrix Lie group, and must satisfy given state and control action constraints pointwise in time. In addition, certain…
Second-order necessary conditions for optimal control problems are considered, where the ``second-order" is in the sense of that Pontryagin's maximum principle is viewed as a first-order necessary optimality condition. A sufficient…
Through the Maximum principle we define the principal eigenvalue for a class of fully-nonlinear operators that are the non-variational equivalent of the p-Laplacian. We also obtain some a priori Holder estimates for non-negative solutions…
We study a class of overdetermined algebraic systems of equations. We prove that the number of distinct solutions equals to the maximal possible if and only if certain matrices are commuting and semisimple. This gives a characterization of…
We prove a maximal-type large deviation principle for dynamical systems with arbitrarily slow polynomial mixing rates. Also several applications, particularly to billiard systems, are presented.
We provide a proof of strong maximum and minimum principles for fully nonlinear uniformly parabolic equations of second order. The approach is of parabolic nature, slightly differs from the earlier one proposed by L. Nirenberg and does not…
Agreement of the probability current with the resolving paths requires a simplified forward equation for the (unique) Ito paths. Their increments are the most probable rather than expected ones, in accordance with an existing extremum…
We find a maximum principle for general non-Markovian semi-martingales. We do so by describing the adjoint processes with non-anticipating stochastic derivatives in a martingale random field setting. In the case of the L\'evy processes this…
The Augmented Lagrangian Method as an approach for regularizing inverse problems received much attention recently, e.g. under the name Bregman iteration in imaging. This work shows convergence (rates) for this method when Morozov's…
We study the validity of the comparison and maximum principles, and their relation with principal eigenvalues, for a class of degenerate nonlinear operators that are extremal among operators with one dimensional fractional diffusion.
We consider a class of optimization problems that involve determining the maximum value that a function in a particular class can attain subject to a collection of difference constraints. We show that a particular linear programming…
Some optimization problems coming from the Differential Geometry, as for example, the minimal submanifolds problem and the harmonic maps problem are solved here via interior solutions of appropriate multitime optimal control problems.…
In this paper, we prove a maximum principle for the $p$-Laplacian with a sign-changing weight. As an application of this maximum principle, we study the existence of one-sign solutions for a class of quasilinear elliptic problems.
We establish necessary conditions of optimality for discrete-time infinite-horizon optimal control in presence of constraints at infinity. These necessary conditions are in form of weak and strong Pontryagin principles. We use a functional…
We derive a first order optimality condition for a class of agent-based systems, as well as for their mean-field counterpart. A relevant difficulty of our analysis is that the state equation is formulated on possibly infinite-dimensional…