1 - Outline of Classical Optimization Methods

Abstract

This chapter provides a brief description of contemporary optimization methods and approaches which are applied throughout this book to improve the performance of thermal, mechanical, chemical, and environmental systems. We optimize profit or cost criteria subject to equality and/or inequality constraints by applying search approaches, methods of static and dynamic optimization, and using some stochastic techniques. With these methods and approaches, we investigate unique optimal properties of neural networks, cascades, multilevel systems of complex topology, etc. Throughout the chapters of this book, optimization problems and goal criteria are formulated, and optimal solutions are found for unit operations and chemical reactors. Our concise review of optimization tools outlines the methods based on differential calculus, Lagrange multipliers, mathematical programming, iterative approaches, dynamic algorithms, and some stochastic optimization techniques. They are applied in the book to processes with energy yield and conversion, modeled with the help of classical and finite-time thermodynamics and second-law approaches. Throughout the book special attention is paid to fluid-solid catalytic systems with particulate solids as well as to complex multiphase reaction-regeneration systems with deactivated sorbents and catalysts.