SI “Deterministic and Stochastic Variational Principles and Applications”. December 2015

Abstract

Variational methods are important tools for deriving optimality conditions and corresponding algorithms for solving optimization problems. Ekeland’s variational principle is a deep assertion about the existence of an exact solution of a perturbed optimization problem in a neighborhood of an approximate solution of the original problem. The aim of this special issue was to discuss new variational approaches from the theoretical as well as computational point of view. Furthermore, we are interested in applications of the variational methods for deterministic and stochastic models, especially in approximation theory and optimal control. In the special issue the importance of variational methods in optimization and stochastics is described.We present newdevelopments on the field of deterministic and stochastic variational methods including applications in mathematics and economics. Most of the papers in the special issue are dealing with optimal control and state estimates problems in the deterministic as well as stochastic case and maximum principles (Abdelmadjid Abba: On Mean-field Partial Information Maximum Principle of Optimal Control for Stochastic Systems with Levy Processes, Vo Anh: Least-Squares Estimation of Multifractional Random Fields in a Hilbert-Valued Context, Brigitte Breckner: Multiple solutions of Dirichlet problems on the Sierpinski gasket, Ioana Ciotir: A variational approach to Neumann stochastic semi-linear equations modelling the thermostatic control, CsabaVarga, Hannelore Lisei: Amultiplicity result for a class of elliptic problems on a compact Riemannian manifold, Tina Engler: On Investment Consumption Modeling with Jump Process Extensions for Productive Sectors, Diana