Application of Optimization Methods to the Solution of Operator Equations

Abstract

A very short survey is given about an important field of the application of optimization theory for solving operator equations, in particular differential- and integral equations. Optimization methods have been applied to nearly all sciences in which one has used mathematical formulations. Operations research is closely connected with many problems of economy. Other applications were given by lecturers of these conference. Therefore it may be allowed to mention a very wide area of applications of optimization methods, in which one has a great success during the last ten to twenty years. In the opinion of the author there are very important applications of optimization techniques. As example I mention the solution of operator equations, for instance linear and nonlinear ordinary and partial differential equations and integral equations for functions of one or several variables, and by these means one can solve many problems in physics, engineering and other sciences; for many problems optimization methods are the only ones for obtaining exact error bounds for approximate solutions.