Related papers: Equilibrium problems for vector potentials with se…
This paper considers mathematical programs, whose constraints are expressed by a parameterized vector equilibrium problem. The latter is a well recognized framework, which is able to cover multicriteria optimization, vector variational…
It is a well-known conjecture in $\beta$-models and in their discrete counterpart that, generically, external potentials should be ``off-critical'' (or, equivalently, ``regular''). Exploiting the connection between minimizing measures and…
This work concerns superharmonic perturbations of a Gaussian measure given by a special class of positive weights in the complex plane of the form $w(z) = \exp(-|z|^2 + U^{\mu}(z))$, where $U^{\mu}(z)$ is the logarithmic potential of a…
We prove existence of weak solutions to the obstacle problem for semilinear wave equations (including the fractional case) by using a suitable approximating scheme in the spirit of minimizing movements. This extends the results in [9],…
A method for testing $G_\mu$-stability of relative equilibria in Hamiltonian systems of the form "kinetic + potential energy" is presented. This method extends the Reduced Energy-Momentum Method of Simo et al. to the case of non-free group…
In this work, we establish that discontinuous Galerkin methods are capable of producing reliable approximations for a broad class of nonlinear variational problems. In particular, we demonstrate that these schemes provide essential…
We study compressible and incompressible nonlinear elasticity variational problems in a general context. Our main result gives a sufficient condition for an equilibrium to be a global energy minimizer, in terms of convexity properties of…
In this paper we characterise the equilibrium measure for a nonlocal and anisotropic weighted energy describing the interaction of positive dislocations in the plane. We prove that the minimum value of the energy is attained by a measure…
We consider systems of weakly coupled Schr\"odinger equations with nonconstant potentials and we investigate the existence of nontrivial nonnegative solutions which concentrate around local minima of the potentials. We obtain sufficient and…
In this article, we provide a new algorithm for solving constraint satisfaction problems over templates with few subpowers, by reducing the problem to the combination of solvability of a polynomial number of systems of linear equations over…
We investigate partial regularity for vector valued local minimizers of double phase functionals, under vectorial obstacle type constraints satisfying appropriate topological properties.
In this paper, we study the asymptotic behaviour of minimizing solutions of a Ginzburg-Landau type functional with a positive weight and with convex potential near $0$ and we estimate the energy in this case. We also generalize a lower…
For a finite collection $\mathbf A=(A_i)_{i\in I}$ of locally closed sets in $\mathbb R^n$, $n\geqslant3$, with the sign $\pm1$ prescribed such that the oppositely charged plates are mutually disjoint, we consider the minimum energy problem…
We present a multidimensional optimization problem that is formulated and solved in the tropical mathematics setting. The problem consists of minimizing a nonlinear objective function defined on vectors over an idempotent semifield by means…
In this paper, we generalize the chance optimization problems and introduce constrained volume optimization where enables us to obtain convex formulation for challenging problems in systems and control. We show that many different problems…
We study measures and point configurations optimizing energies based on multivariate potentials. The emphasis is put on potentials defined by geometric characteristics of sets of points, which serve as multi-input generalizations of the…
In this work, we focus on separable convex optimization problems with linear and box constraints and compute the solution in closed-form as a function of some Lagrange multipliers that can be easily computed in a finite number of…
This paper explores some sufficient conditions for the enhanced solvability of strong vector equilibrium problems, which can be established via a variational approach. Enhanced solvability here means existence of solutions, which are strong…
We study the equilibrium measure for a logarithmic potential in the presence of an external field V*(x) + tp(x), where t is a parameter, V*(x) is a smooth function and p(x) a monic polynomial. When p(x) is of an odd degree, the equilibrium…
The existence of compactly supported global minimisers for continuum models of particles interacting through a potential is shown under almost optimal hypotheses. The main assumption on the potential is that it is catastrophic, or not…