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Applications of variational methods are typically restricted to conservative systems. Some extensions to dissipative systems have been reported too but require ad hoc techniques such as the artificial doubling of the dynamical variables.…
The paper is devoted to a comprehensive study of composite models in variational analysis and optimization the importance of which for numerous theoretical, algorithmic, and applied issues of operations research is difficult to overstate.…
We consider a variational convex relaxation of a class of optimal partitioning and multiclass labeling problems, which has recently proven quite successful and can be seen as a continuous analogue of Linear Programming (LP) relaxation…
We establish the dual notions of scaling and saturation from geometric control theory in an infinite-dimensional setting. This generalization is applied to the low-mode control problem in a number of concrete nonlinear partial differential…
We apply symmetry and invariance methods to analyse systems of difference equations. Non trivial symmetries are derived and their exact solutions obtained.
In this note we devise and analyse well-posed variational formulations and operator theoretical methods for boundary value problems associated to the biharmonic operator. Of particular interest are Neumann type and over- and underdetermined…
We show global uniqueness of the solution to a class of constrained variational problems, using scaling properties. This is used to establish the essential uniqueness of solutions of a large deviations problem in multiple dimensions. The…
Variational inequalities are an important mathematical tool for modelling free boundary problems that arise in different application areas. Due to the intricate nonsmooth structure of the resulting models, their analysis and optimization is…
In this paper, we consider the classic stochastic (dynamic) knapsack problem, a fundamental mathematical model in revenue management, with general time-varying random demand. Our main goal is to study the optimal policies, which can be…
The discrete, the quantum, and the continuous calculus of variations, have been recently unified and extended by using the theory of time scales. Such unification and extension is, however, not unique, and two approaches are followed in the…
Whereas in a coordinate-dependent setting the Euler-Lagrange equations establish necessary conditions for solving variational problems in which both the integrands of functionals and the resulting paths are assumed to be sufficiently…
Distribution functions of many static transport equations are found using the Maximum Entropy Principle. The equations of constraint which contain the relevant dynamical information are simply the low-lying moments of the distributions.…
We consider a class of integer-constrained optimization problems governed by partial differential equation (PDE) constraints and regularized via total variation (TV) in the context of topology optimization. The presence of discrete design…
Fractional operators play an important role in modeling nonlocal phenomena and problems involving coarse-grained and fractal spaces. The fractional calculus of variations with functionals depending on derivatives and/or integrals of…
Persistence modules are representations of products of totally ordered sets in the category of vector spaces. They appear naturally in the representation theory of algebras, but in recent years they have also found applications in other…
The aim of this work is to develop general optimization methods for finite difference schemes used to approximate linear differential equations. The specific case of the transport equation is exposed. In particular, the minimization of the…
Systems of ordinary differential equations (or dynamical forms in Lagrangian mechanics), induced by embeddings of smooth fibered manifolds over one-dimensional basis, are considered in the class of variational equations. For a given…
We introduce discretizations of infinite-dimensional optimization problems with total variation regularization and integrality constraints on the optimization variables. We advance the discretization of the dual formulation of the total…
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…
In this work we propose a new and more general approach to the calculus of variations on time scales that allows to obtain, as particular cases, both delta and nabla results. More precisely, we pose the problem of minimizing or maximizing…