Introduction to Optimization Methods

In: Chapman and Hall Mathematics Series

Abstract

1 The optimization problem -- 1.1 Introduction -- 1.2 Problem definition -- 1.3 Optimization in one dimension -- 1.4 Optimization in n dimensions -- 2 Single variable optimization -- 2.1 Review of methods -- 2.2 The Fibonacci search -- 2.3 The Golden Section search -- 2.4 The Algorithm of Davies, Swann, and Campey -- 3 Multi-variable optimization -- 3.1 Introduction -- 3.2 Search methods -- 3.3 Gradient methods -- 4 Advanced methods -- 4.1 Introduction -- 4.2 General considerations -- 4.3 Advanced search methods -- 4.4 Advanced gradient methods -- 4.5 Minimax methods -- 5 Constrained optimization -- 5.1 Introduction -- 5.2 The Kuhn-Tucker conditions -- 5.3 Constrained optimization techniques -- 5.4 Direct search methods with constraints -- 5.5 Small step gradient methods -- 5.6 Sequential unconstrained methods -- 5.7 Large step gradient methods -- 5.8 Lagrangian methods -- 5.9 General considerations -- 5.10 Conclusion -- References -- Further reading.