Approximation Methods in Optimization of Nonlinear Systems

✍ Scribed by Peter I. Kogut; Olga P. Kupenko

• Publisher: De Gruyter
• Year: 2019
• Tongue: English
• Leaves: 352
• Series: De Gruyter Series in Nonlinear Analysis and Applications; 32
• Category: Library

✦ Synopsis

The monograph addresses some problems particularly with regard to ill-posedness of boundary value problems and problems where we cannot expect to have uniqueness of their solutions in the standard functional spaces. Bringing original and previous results together, it tackles computational challenges by exploiting methods of approximation and asymptotic analysis and harnessing differences between optimal control problems and their underlying PDEs

Renowned Authors

✦ Table of Contents

Preface
Contents
Introduction
1. Optimal Distributed Control Problem for an Ill-Posed Strongly Nonlinear Elliptic Equation with p-Laplace Operator and L¹-Type of Nonlinearity
2. On Approximation of One Class of Optimal Control Problems for Strongly Nonlinear Elliptic Equations with p-Laplace Operator
3. Neumann Boundary Optimal Control Problem for Strongly Nonlinear Elliptic Equation with p-Laplace Operator
4. Asymptotic Analysis of Optimal Neumann Boundary Control Problem in Domain with Boundary Oscillation for Elliptic Equation with Exponential Non-Linearity
5. On Optimal and Quasi-Optimal Controls in Coefficients for Multi-Dimensional Thermistor Problem with Mixed Dirichlet-Neumann Boundary Conditions
6. Approximation of an Optimal Control Problem in Coefficient for Variational Inequality with Anisotropic p-Laplacian
7. On Unbounded Optimal Controls in Coefficients for Ill-Posed Elliptic Dirichlet Boundary Value Problems
8. On Optimal L¹-Control in Coefficients for Quasi-Linear Dirichlet Boundary Value Problem with BMO-Anisotropic p-Laplacian
Bibliography