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A numerical method for the computation of the best constant in a Sobolev inequality involving the spaces H2(Ω) and $C^{0}(\overline{\Omega})$ is presented. Green’s functions corresponding to the solution of Poisson problems are used to express the solution. This (kind of) non-smooth eigenvalue problem is then formulated as a constrained optimization problem and solved with two different strategies:...
A model coupling differential equations and a sequence of constrained optimization problems is proposed for the simulation of the evolution of a population of particles at equilibrium interacting through a common medium.The first order optimality conditions of the optimization problems relaxed with barrier functions are coupled with the differential equations into a system of differential-algebraic...
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