MULTIOBJECTIVE OPTIMISATION AND CONTROL
CON TEN TS 1 IN TRO DUCTION 1 1 1 MULTIOB JECTIV E OPTIMISATION 1 1 1 1 CONSTRAINED OPTIMISATION 1 1 1 2 CON V EN TIONAL MULTIOB JECTIV E OPTIMISATION 2 1 1 3 METHO D OF INEQUALITIES 7 1 1 4 MULTIOB JECTIV E GENETIC ALGORITHMS 9 1 2 MULTIOB JECTIV E CON TROL 10 1 2 1 CON ICTS AND T RADE OS IN CON TROL SYSTEMS 11 1 2 2 MULTIOB JECTIV E ROBUST CON TROL 14 1 2 3 MULTIOB JECTIV E CRITICAL CON TROL 15 1 2 4 MULTIOB JECTIV E EIGENSTRUCTURE ASSIGNMEN T 16 1 2 5 MULTIOB JECTIV E PID CON TROL 16 1 2 6 MULTIOB JECTIV E OPTIMISATION OF CON TROLLER IMPLEMEN TATIONS 17 1 2 7 MULTIOB JECTIV E NONLINEAR IDEN TICATION 18 1 2 8 MULTIOB JECTIV E F AULT DETECTION 19 1 3 OUTLINE OF THE BO OK 20 2 NONLINEAR OPTIMISATION 23 2 1 ONE DIMENSIONAL OPTIMISATION 23 2 1 1 THE DIC HOTOM Y METHO D WITH DERIV ATIV ES 23 2 1 2 THE DIC HOTOM Y METHO D WITHOUT DERIV ATIV ES 25 2 1 3 THE FIB ONACCI METHO D 26 2 1 4 THE GOLDEN SECTION SEARC H METHO D 31 2 2 OPTIMISATION CONDITIONS 32 2 2 1 NECESSARY CONDITIONS FOR LO CAL OPTIMALIT Y 32 2 2 2 SU CIEN T CONDITIONS FOR LO CAL OPTIMALIT Y 34 VII VIII CONTENTS 2 3 UNCONSTRAINED OPTIMISATION METHO DS 34 2 3 1 STEEP EST DECEN T METHO D 34 2 3 2 NEWTON S METHO D 38 2 3 3 QUASI NEWTON S METHO DS 41 2 4 SUMMARY 44 3 CONSTRAINED OPTIMISATION 45 3 1 IN TRO DUCTION 45 3 2 OPTIMALIT Y CONDITIONS 46 3 2 1 BASIC CONCEPTS 46 3 2 2 KUHN T UC K ER NECESSARY CONDITION 47 3 2 3 SECOND ORDER SU CIEN T CONDITIONS 48 3 3 PRIMAL METHO DS 52 3 3 1 SEQUEN TIAL LINEAR PROGRAMMING 52 3 3 2 SEQUEN TIAL QUADRATIC PROGRAMMING 55 3 4 DUAL METHO DS 60 3 4 1 LAGRANGEAN METHO DS 61 3 4 2 METHO D OF EXTERIOR P ENALTIES 64 3 4 3 METHO D OF IN TERIOR P ENALTIES 68 3 5 SUMMARY 71 4 MULTIPLE OB JECTIV E OPTIMISATION 73 4 1 IN TRO DUCTION 73 4 2 BASIC CONCEPTS AND METHO DS 74 4 2 1 CONCEPTS AND DENITIONS 74 4 2 2 METHO D CLASSICATION 77 4 2 3 SIMPLE W EIGH TING METHO D 78 4 3 P NORM METHO DS 82 4 3 1 MINIMAX IDEAL P OIN T METHO D 82 4 3 2 GOAL A TTAINMEN T METHO D 89 4 3 3 GOAL PROGRAMMING 91 4 3 4 THE MINIMAX REFERENCE P OIN T METHO D 95 4 4 IN TERACTIV E METHO DS 103 4 4 1 GEORION S METHO D 103 4 4 2 THE STEM METHO D 108 4 4 3 THE ISTM METHO D 112 4 4 4 THE GRADIEN T PRO JECTION METHO D 116 4 5 SUMMARY 123 5 GENETIC ALGORITHMS AND OPTIMISATION 125 5 1 IN TRO DUCTION 125