Nonstandard Models and Optimization
arXiv:0805.3947
Abstract
This is an overview of a few possibilities that are open by model theory in applied mathematics. Most attention is paid to the present state and frontiers of the Cauchy method of majorants, approximation of operator equations with finite-dimensional analogs, and the Lagrange multiplier principle in multiobjective decision making.
An extended version of a talk prepared for the International Conference "Methods of Logic in Mathematics V," June 1--6, 2008, St. Petersburg