Sensitivity functionals in convex optimization problem

Adaptive Optimization of Convex Functionals in Banach Spaces

This paper is concerned with optimization or minimization problems that are governed by operator equations, such as partial differential or integral equations, and thus are naturally formulated in an infinite dimensional function space V . We first construct a prototype algorithm of steepest descent type in V and prove its convergence. By using a Riesz basis in V we can transform the minimizati...

Design optimization based on state problem functionals

This paper presents a general mathematical structure for design optimization problems, where state problem functionals are used as design objectives. It extends to design optimization the general model of physical theories pioneered by Tonti [38, 39] and Oden and Reddy [31, 32]. It turns out that the classical structural optimization problem of compliance minimization is a member of the treated...

On the Minimization Problem of Sub-linear Convex Functionals

The study of the convergence to equilibrium of solutions to FokkerPlanck type equations with linear diffusion and super-linear drift leads in a natural way to a minimization problem for an energy functional (entropy) which relies on a sub-linear convex function. In many cases, conditions linked both to the non-linearity of the drift and to the space dimension allow the equilibrium to have a sin...

Generalized convex functionals

This paper studies functionals defined by multiple integrals associated to differential forms on the jet bundle of first order corresponding to some Riemannian manifolds; the domain of these functionals consists in submanifold maps satisfying certain conditions of integrability. Our idea is to give geometric properties to the domain of a functional allowing us to properly define convexity. The ...

Approximation of Non-convex Functionals in Gbv Approximation of Non-convex Functionals in Gbv