Nonlinear Multiobjective Optimization: A Generalized Homotopy Approach

by Claus Hillermeier

Overview

Arguably, many industrial optimization problems are of the multiobjective type. The present work, after providing a survey of the state of the art in multiobjective optimization, gives new insight into this important mathematical field by consequently taking up the viewpoint of differential geometry. This approach, unprecedented in the literature, very naturally results in a generalized homotopy method for multiobjective optimization which is theoretically well-founded and numerically efficient. The power of the new method is demonstrated by solving two real-life problems of industrial optimization.

The book presents recent results obtained by the author and is aimed at mathematicians, scientists, students and practitioners interested in optimization and numerical homotopy methods.

Product Details

ISBN-13:	9783034895019
Publisher:	Birkhäuser Basel
Publication date:	11/10/2012
Series:	International Series of Numerical Mathematics , #135
Edition description:	Softcover reprint of the original 1st ed. 2001
Pages:	135
Product dimensions:	6.10(w) x 9.25(h) x 0.01(d)

Table of Contents

1 Introduction.- 2 Vector Optimization in Industrial Applications.- 3 Principles and Methods of Vector Optimization.- 4 The Connection with Scalar-Valued Optimization.- 5 The Manifold of Stationary Points.- 6 Homotopy Strategies.- 7 Numerical Results.