Related papers: Double Well Potential Function and Its Optimizatio…

The paper addresses the study and applications of a broad class of extended-real-valued functions, known as optimal value or marginal functions, which are frequently appeared in variational analysis, parametric optimization, and a variety…

In this work we present two particular cases of the general duality result for linear optimisation problems over signed measures with infinitely many constraints in the form of integrals of functions with respect to the decision variables…

This paper investigates minimax quadratic programming problems with coupled inequality constraints. By leveraging a duality theorem, we develop a dual algorithm that extends the dual active set method to the minimax setting, transforming…

In this paper, a class of generalized backward doubly stochastic differential equations whose coefficient contains the subdifferential operators of two convex functions (also called generalized backward doubly stochastic variational…

A nonlocal Cahn-Hilliard model with a nonsmooth potential of double-well obstacle type that promotes sharp interfaces in the solution is presented. To capture long-range interactions between particles, a nonlocal Ginzburg-Landau energy…

The paper arXiv:1804.11290 contains well-posedness and regularity results for a system of evolutionary operator equations having the structure of a Cahn-Hilliard system. The operators appearing in the system equations were fractional…

Let $(\mathcal{X},d,\mu)$ be a doubling metric measure space in the sense of R. R. Coifman and G. Weiss, $L$ a non-negative self-adjoint operator on $L^2(\mathcal{X})$ satisfying the Davies--Gaffney estimate, and $X(\mathcal{X})$ a ball…

In this paper, we propose a method of fundamental solutions for the problem of two-dimensional potential flow in a doubly-periodic domain. The solution involves a doubly-periodic function, to which it is difficult to give an approximation…

Using examples of a D=2 chiral scalar and a duality-symmetric formulation of D=4 Maxwell theory we study duality properties of actions for describing chiral bosons. In particular, in the D=4 case, upon performing a duality transform of an…

Local solutions for variational and quasi-variational inequalities are usually the best type of solutions that could practically be obtained when in case of lack of convexity or else when available numerical techniques are too limited for…

We consider a general energy functional for phase coexistence models, which comprises the case of Banach norms in the gradient term plus a double-well potential. We establish density estimates for $Q$-minima. Namely, the state parameters…

The density of polynomials in a weighted space of infinitely differentiable functions in a multidimensional real space is proved under minimal conditions on weight functions and on differences between weight functions. We apply this result…

We consider the standard optimistic bilevel optimization problem, in particular upper- and lower-level constraints can be coupled. By means of the lower-level value function, the problem is transformed into a single-level optimization…

Let $R$ be a Cohen-Macaulay local ring with a canonical module $\omega_R$. Let $I$ be an $\m$-primary ideal of $R$ and $M$, a maximal Cohen-Macaulay $R$-module. We call the function $n\longmapsto \ell (\Hom_R(M,{\omega_R}/{I^{n+1}…

We consider the problem of maximizing a monotone nondecreasing set function under multiple constraints, where the constraints are also characterized by monotone nondecreasing set functions. We propose two greedy algorithms to solve the…

The aim of this paper is to develop an efficient algorithm for solving a class of unconstrained nondifferentiable convex optimization problems in finite dimensional spaces. To this end we formulate first its Fenchel dual problem and…

We prove that, any problem of minimization of proper lower semicontinuous function defined on a normal Hausdorff space, is canonically equivalent to a problem of minimization of a proper weak * lower semicontinuous convex function defined…

We study the mixed Dirichlet-Neumann problem for the Laplace equation in the complement of a bounded convex polygonal quadrilateral in the extended complex plane. The Dirichlet\,/\,Neumann conditions at opposite pairs of sides are $\{0,1\}$…

DR-submodular functions encompass a broad class of functions which are generally non-convex and non-concave. We study the problem of minimizing any DR-submodular function, with continuous and general integer variables, under box constraints…

Double Field Theory describes the NS-NS sector of string theory and lives on a doubled spacetime. The theory has a local gauge symmetry generated by a generalization of the Lie derivative for doubled coordinates. For the action to be…