ALGORITHMS FOR APPROXIMATION OF SOLUTIONS OF EQUATIONS INVOLVING NONLINEAR MONOTONE-TYPE AND MULTI-VALUED MAPPINGS

📄 Project Abstract

It is well know that many physically signi_x000C_cant problems in di_x000B_erent areas of research can be transformed into an equation of the form Au = 0; (0.0.1) where A is a nonlinear monotone operator from a real Banach space E into its dual E_x0003_. For instance, in optimization, if f : E ! R [ f+1g is a convex, G^ateaux di_x000B_erentiable function and x_x0003_ is a minimizer of f, then f0(x_x0003_) = 0. This gives a criterion for obtaining a minimizer of f explicitly. However, most of the operators that are involved in several signi_x000C_cant optimization problems are not di_x000B_erentiable. For instance, the absolute value function x 7! jxj has a minimizer, which, in fact, is 0. But, the absolute value function is not di_x000B_erentiable at 0. So, in a case where the operator under consideration is not di_x000B_erentiable, it becomes di_x000E_cult to know a minimizer even when it exists. Thus, the above characterization only works for di_x000B_erentiable operators. A generali...