Related papers: A minimizing principle for the Poisson-Boltzmann e…

A major obstacle to non-convex optimization is the problem of getting stuck in local minima. We introduce a novel metaheuristic to handle this issue, creating an alternate Hamiltonian that shares minima with the original Hamiltonian only…

Bose-Einstein condensates with tunable interatomic interactions have been studied intensely in recent experiments. The investigation of the collapse of a condensate following a sudden change in the nature of the interaction from repulsive…

Weak sharp minimality is a notion emerged in optimization, whose utility is largeley recognized in the convergence analysis of algorithms for solving extremum problems as well as in the study of the perturbation behaviour of such problems.…

We provide a dynamic programming principle for stochastic optimal control problems with expectation constraints. A weak formulation, using test functions and a probabilistic relaxation of the constraint, avoids restrictions related to a…

We consider the sharp Sobolev-Poincar\'e constant for the embedding of $W^{1,2}_0(\Omega)$ into $L^q(\Omega)$. We show that such a constant exhibits an unexpected dual variational formulation, in the range $1<q<2$. Namely, this can be…

We prove a Pontryagin Maximum Principle for optimal control problems in the space of probability measures, where the dynamics is given by a transport equation with non-local velocity. We formulate this first-order optimality condition using…

In the present research, a variational technique to modifying the Poisson equation is presented, expanding its modelling capabilities to include a wider range of physical processes and resonant structures. The study examines the…

We connect two different generalizations of Boltzmann's kinetic theory by requiring the same stationary solution. Non-extensive statistics can be produced by either using corresponding collision rates nonlinear in the one-particle densities…

We consider the Boltzmann equation with the soft potential and angular cutoff. Inspired by the methods from dispersive PDEs, we establish its sharp local well-posedness and ill-posedness in $H^{s}$ Sobolev space. We find the…

We consider several local versions of the doubling condition and Poincar\'e inequalities on metric spaces. Our first result is that in proper connected spaces, the weakest local assumptions self-improve to semilocal ones, i.e. holding…

We consider the spatially inhomogeneous non-cutoff Boltzmann equation with hard potentials in the non-perturbative setting. For initial data with polynomial decay in the velocity variable, we establish the local-in-time existence and…

We derive the existence and uniqueness of the generalized backward doubly stochastic differential equation with sub-differential of a lower semi-continuous convex function under a non Lipschitz condition. This study allows us give a…

In this article we develop a duality principle and concerning computational method for a structural optimization problem in elasticity. We consider the problem of finding the optimal topology for an elastic solid which minimizes its…

Discretization of non-linear Poisson-Boltzmann Equation equations results in a system of non-linear equations with symmetric Jacobian. The Newton algorithm is the most useful tool for solving non-linear equations. It consists of solving a…

A broad class of optimization problems can be cast in composite form, that is, considering the minimization of the composition of a lower semicontinuous function with a differentiable mapping. This paper investigates the versatile template…

Non-convex optimization problems have multiple local optimal solutions. Non-convex optimization problems are commonly found in numerous applications. One of the methods recently proposed to efficiently explore multiple local optimal…

We consider the problem of approximating the solution of variational problems subject to the constraint that the admissible functions must be convex. This problem is at the interface between convex analysis, convex optimization, variational…

A fundamental problem in numerical analysis and approximation theory is approximating smooth functions by polynomials. A much harder version under recent consideration is to enforce bounds constraints on the approximating polynomial. In…

We present a derivation of generalized Poisson-Boltzmann equations starting {from} classical theories of binary fluid mixtures, employing an approach based on the Legendre transform as recently applied to the case of local descriptions of…

We consider a nonlocal functional equation that is a generalization of the mathematical model used in behavioral sciences. The equation is built upon an operator that introduces a convex combination and a nonlinear mixing of the function…