Related papers: Bootstrapping Globally Optimal Variational Calculu…
This paper develops a novel approach to necessary optimality conditions for constrained variational problems defined in generally incomplete subspaces of absolutely continuous functions. Our approach involves reducing a variational problem…
We obtain Euler-Lagrange and transversality optimality conditions for higher-order infinite horizon variational problems on a time scale. The new necessary optimality conditions improve the classical results both in the continuous and…
A scheme for generating a family of convex variational principles is developed, the Euler- Lagrange equations of each member of the family formally corresponding to the necessary conditions of optimal control of a given system of ordinary…
We introduce a discrete-time fractional calculus of variations. First and second order necessary optimality conditions are established. Examples illustrating the use of the new Euler-Lagrange and Legendre type conditions are given. They…
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…
In this paper, calculus of variation methods are generalized to find min-max optimal solution of uncertain dynamical systems with uncertain or certain cost. First, a new form of Euler-Lagrange conditions for uncertain systems is presented.…
We prove necessary optimality conditions of Euler-Lagrange type for generalized problems of the calculus of variations on time scales with a Lagrangian depending not only on the independent variable, an unknown function and its delta…
The inverse problem of the calculus of variations consists in determining if the solutions of a given system of second order differential equations correspond with the solutions of the Euler-Lagrange equations for some regular Lagrangian.…
Optimality conditions in the form of a variational inequality are proved for a class of constrained optimal control problems of stochastic differential equations. The cost function and the inequality constraints are functions of the…
This paper provides necessary and sufficient conditions of optimality for variational problems that deal with a fractional derivative with respect to another function. Fractional Euler--Lagrange equations are established for the fundamental…
We consider non-autonomous calculus of variations problems with a state constraint represented by a given closed set. We prove that if the interior of the Clarke tangent cone of the state constraint set is non-empty (this is the constraint…
The fundamental problem of the calculus of variations on time scales concerns the minimization of a delta-integral over all trajectories satisfying given boundary conditions. In this paper we prove the second Euler-Lagrange necessary…
Constrained non-convex optimization is fundamentally challenging, as global solutions are generally intractable and constraint qualifications may not hold. However, in many applications, including safe policy optimization in control and…
Using the recent weighted generalized fractional order operators of Hattaf, a general fractional optimal control problem without constraints on the values of the control functions is formulated and a corresponding (weak) version of…
This paper proposes a new algorithm for solving constrained global optimization problems where both the objective function and constraints are one-dimensional non-differentiable multiextremal Lipschitz functions. Multiextremal constraints…
The fundamental problem of calculus of variations is considered when solutions are differentiable curves on locally convex spaces. Such problems admit an extension of the Euler-Lagrange equations [Orlov 2002] for continuously normally…
This paper concerns optimal control problems for a class of sweeping processes governed by discontinuous unbounded differential inclusions that are described via normal cone mappings to controlled moving sets. Largely motivated by…
We prove existence of radially symmetric solutions and validity of Euler-Lagrange necessary conditions for a class of variational problems such that neither direct methods nor indirect methods of Calculus of Variations apply. We obtain…
Recently, a new class of non-convex optimization problems motivated by the statistical problem of learning an acyclic directed graphical model from data has attracted significant interest. While existing work uses standard first-order…
In this work, we solve a discrete optimal transport problem in a nonuniform environment. To solve the optimal transport problem, we build the cost matrix and then use classical solvers for discrete optimal transport. The challenge is to…