Multiobjective Optimization Introduction Goal Attainment method Algorithm Improvements for Goal Attainment Method Selected Bibliography 3-48 Large-Scale algorithms 4 Trust-Region Methods for Nonlinear Minimization 4-2 Preconditioned Conjugate Gradients 4-5 Linearly Constrained Problems Linear Equality Constraints Box Constraints Nonlinear Least-Squares 4-10 Quadratic Programming 4-11 Linear Least-Squares 4-12 Large-Scale Linear Programming Main algorithm 4-13 processing 4-16 Selected Bibliography 4-17iv Contents Multiobjective Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . 3-38 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-38 Goal Attainment Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-44 Algorithm Improvements for Goal Attainment Method . . . . . 3-45 Selected Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-48 4 Large-Scale Algorithms Trust-Region Methods for Nonlinear Minimization . . . . . . . 4-2 Preconditioned Conjugate Gradients . . . . . . . . . . . . . . . . . . . 4-5 Linearly Constrained Problems . . . . . . . . . . . . . . . . . . . . . . . . 4-7 Linear Equality Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-7 Box Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-7 Nonlinear Least-Squares . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-10 Quadratic Programming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-11 Linear Least-Squares . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-12 Large-Scale Linear Programming . . . . . . . . . . . . . . . . . . . . . 4-13 Main Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-13 Preprocessing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-16 Selected Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-17