Nonstandard Models and Optimization

TL;DR

This paper explores how model theory can be applied to various areas in applied mathematics, focusing on the Cauchy method, operator equation approximation, and multiobjective decision making.

Contribution

It provides an overview of open possibilities in applying model theory to solve complex problems in applied mathematics.

Findings

Highlights current state and frontiers of the Cauchy method of majorants.

Discusses approximation of operator equations with finite-dimensional models.

Examines the Lagrange multiplier principle in multiobjective decision making.

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.