Related papers: Euler-Lagrange equations for multiobjective calcul…
We look for the minimizers of the functional $\jla{\la}(\oo)=\la|\oo|-P(\oo)$ among planar convex domains constrained to lie into a given ring. We prove that, according to the values of the parameter $\la$, the solutions are either a disc…
Langrange duality theorems for vector and set optimization problems which are based on an consequent usage of infimum and supremum (in the sense greatest lower and least upper bounds with respect to a partial ordering) have been recently…
We develop the concept of pluri-Lagrangian structures for integrable hierarchies. This is a continuous counterpart of the pluri-Lagrangian (or Lagrangian multiform) theory of integrable lattice systems. We derive the multi-time Euler…
We investigate finite-dimensional constrained structured optimization problems, featuring composite objective functions and set-membership constraints. Offering an expressive yet simple language, this problem class provides a modeling…
This paper introduces a geometrically constrained variational problem for the area functional. We consider the area restricted to the langrangian surfaces of a Kaehler surface, or, more generally, a symplectic 4-manifold with suitable…
We obtain several Euler-Lagrange equations for variational functionals defined on a set of H\"older curves. The cases when the Lagrangian contains multiple scale derivatives, depends on a parameter, or contains higher-order scale…
Conventional ways to solve optimization problems on low-rank matrix sets which appear in great number of applications ignore its underlying structure of an algebraic variety and existence of singular points. This leads to appearance of…
We investigate variational problems in large-strain magnetoelasticity, both in the static and in the quasistatic setting. The model contemplates a mixed Eulerian-Lagrangian formulation: while deformations are defined on the reference…
Euler's elastica model has been extensively studied and applied to image processing tasks. However, due to the high nonlinearity and nonconvexity of the involved curvature term, conventional algorithms suffer from slow convergence and high…
In this paper we will discuss some new developments in the design of numerical methods for optimal control problems of Lagrangian systems on Lie groups. We will construct these geometric integrators using discrete variational calculus on…
Optimization problems with convex quadratic cost and polyhedral constraints are ubiquitous in signal processing, automatic control and decision-making. We consider here an enlarged problem class that allows to encode logical conditions and…
In this note, three Lagrange multiplier rules introduced in the literature for set valued optimization problems are compared. A generalization of all three results is given which proves that under rather mild assumptions, $x$ is a weak…
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…
In this paper we define a notion of calibration for an equivalent approach to the classical Steiner problem in a covering space setting and we give some explicit examples. Moreover we introduce the notion of calibration in families: the…
We consider a class of integral functionals with Musielak-Orlicz type variable growth, possibly linear in some regions of the domain. This includes $p(x)$ power-type integrands with $p(x)\ge 1$ as well as double-phase $p\!-\!q$ integrands…
We propose general notions to deal with large scale polynomial optimization problems and demonstrate their efficiency on a key industrial problem of the twenty first century, namely the optimal power flow problem. These notions enable us to…
We consider the problem of minimizing the sum of submodular set functions assuming minimization oracles of each summand function. Most existing approaches reformulate the problem as the convex minimization of the sum of the corresponding…
This paper considers the Euler-Lagrange equations satisfied by the critical points of a large class of conformally invariant extrinsic energies for 4-manifolds immersed into Euclidean space (any codimension). Using invariances and Noether's…
For an elliptic, semilinear differential operator of the form $S(u) = A : D^2 u + b(x, u , Du)$, consider the functional $E_\infty(u) = \mathop{\mathrm{ess \, sup}}_\Omega |S(u)|$. We study minimisers of $E_\infty$ for prescribed boundary…
Motivated by applications to cell biology, we study the constrained minimization of the Helfrich energy among closed surfaces confined to a container. We show existence of minimizers in the class of bubble trees of spherical weak branched…