Nonlinear Optimization with Financial Applications (eBook)

output/0983.tif 2
output/0985.tif 3
output/0986.tif 4
output/0987.tif 5
output/0988.tif 6
output/0989.tif 7
output/0990.tif 8
output/0991.tif 9
output/0993.tif 10
output/0995.tif 11
output/0996.tif 12
output/0997.tif 13
output/0998.tif 14
output/0999.tif 15
output/1001.tif 16
output/1002.tif 17
output/1003.tif 18
output/1004.tif 19
output/1005.tif 20
output/1006.tif 21
output/1007.tif 22
output/1008.tif 23
output/1009.tif 24
output/1010.tif 25
output/1011.tif 26
output/1012.tif 27
output/1013.tif 28
output/1014.tif 29
output/1015.tif 30
output/1016.tif 31
output/1017.tif 32
output/1018.tif 33
output/1019.tif 34
output/1020.tif 35
output/1021.tif 36
output/1022.tif 37
output/1023.tif 38
output/1024.tif 39
output/1025.tif 40
output/1026.tif 41
output/1027.tif 42
output/1028.tif 43
output/1029.tif 44
output/1030.tif 45
output/1031.tif 46
output/1032.tif 47
output/1033.tif 48
output/1034.tif 49
output/1035.tif 50
output/1036.tif 51
output/1037.tif 52
output/1038.tif 53
output/1039.tif 54
output/1040.tif 55
output/1041.tif 56
output/1042.tif 57
output/1043.tif 58
output/1044.tif 59
output/1045.tif 60
output/1046.tif 61
output/1047.tif 62
output/1048.tif 63
output/1049.tif 64
output/1050.tif 65
output/1051.tif 66
output/1052.tif 67
output/1053.tif 68
output/1054.tif 69
output/1055.tif 70
output/1056.tif 71
output/1057.tif 72
output/1058.tif 73
output/1059.tif 74
output/1060.tif 75
output/1061.tif 76
output/1062.tif 77
output/1063.tif 78
output/1064.tif 79
output/1065.tif 80
output/1066.tif 81
output/1067.tif 82
output/1068.tif 83
output/1069.tif 84
output/1070.tif 85
output/1071.tif 86
output/1072.tif 87
output/1073.tif 88
output/1074.tif 89
output/1075.tif 90
output/1076.tif 91
output/1077.tif 92
output/1078.tif 93
output/1079.tif 94
output/1080.tif 95
output/1081.tif 96
output/1082.tif 97
output/1083.tif 98
output/1084.tif 99
output/1085.tif 100
output/1086.tif 101
output/1087.tif 102
output/1088.tif 103
output/1089.tif 104
output/1090.tif 105
output/1091.tif 106
output/1092.tif 107
output/1093.tif 108
output/1094.tif 109
output/1095.tif 110
output/1096.tif 111
output/1097.tif 112
output/1098.tif 113
output/1099.tif 114
output/1100.tif 115
output/1101.tif 116
output/1102.tif 117
output/1103.tif 118
output/1104.tif 119
output/1105.tif 120
output/1106.tif 121
output/1107.tif 122
output/1108.tif 123
output/1109.tif 124
output/1110.tif 125
output/1111.tif 126
output/1112.tif 127
output/1113.tif 128
output/1114.tif 129
output/1115.tif 130
output/1116.tif 131
output/1117.tif 132
output/1118.tif 133
output/1119.tif 134
output/1120.tif 135
output/1121.tif 136
output/1122.tif 137
output/1123.tif 138
output/1124.tif 139
output/1125.tif 140
output/1126.tif 141
output/1127.tif 142
output/1128.tif 143
output/1129.tif 144
output/1130.tif 145
output/1131.tif 146
output/1132.tif 147
output/1133.tif 148
output/1134.tif 149
output/1135.tif 150
output/1136.tif 151
output/1137.tif 152
output/1138.tif 153
output/1139.tif 154
output/1140.tif 155
output/1141.tif 156
output/1142.tif 157
output/1143.tif 158
output/1144.tif 159
output/1145.tif 160
output/1146.tif 161
output/1147.tif 162
output/1148.tif 163
output/1149.tif 164
output/1150.tif 165
output/1151.tif 166
output/1152.tif 167
output/1153.tif 168
output/1154.tif 169
output/1155.tif 170
output/1156.tif 171
output/1157.tif 172
output/1158.tif 173
output/1159.tif 174
output/1160.tif 175
output/1161.tif 176
output/1162.tif 177
output/1163.tif 178
output/1164.tif 179
output/1165.tif 180
output/1166.tif 181
output/1167.tif 182
output/1168.tif 183
output/1169.tif 184
output/1170.tif 185
output/1171.tif 186
output/1172.tif 187
output/1173.tif 188
output/1174.tif 189
output/1175.tif 190
output/1176.tif 191
output/1177.tif 192
output/1178.tif 193
output/1179.tif 194
output/1180.tif 195
output/1181.tif 196
output/1182.tif 197
output/1183.tif 198
output/1184.tif 199
output/1185.tif 200
output/1186.tif 201
output/1187.tif 202
output/1188.tif 203
output/1189.tif 204
output/1190.tif 205
output/1191.tif 206
output/1192.tif 207
output/1193.tif 208
output/1194.tif 209
output/1195.tif 210
output/1196.tif 211
output/1197.tif 212
output/1198.tif 213
output/1199.tif 214
output/1200.tif 215
output/1201.tif 216
output/1202.tif 217
output/1203.tif 218
output/1204.tif 219
output/1205.tif 220
output/1206.tif 221
output/1207.tif 222
output/1208.tif 223
output/1209.tif 224
output/1210.tif 225
output/1211.tif 226
output/1212.tif 227
output/1213.tif 228
output/1214.tif 229
output/1215.tif 230
output/1216.tif 231
output/1217.tif 232
output/1218.tif 233
output/1219.tif 234
output/1220.tif 235
output/1221.tif 236
output/1222.tif 237
output/1223.tif 238
output/1224.tif 239
output/1225.tif 240
output/1226.tif 241
output/1227.tif 242
output/1228.tif 243
output/1229.tif 244
output/1230.tif 245
output/1231.tif 246
output/1232.tif 247
output/1233.tif 248
output/1234.tif 249
output/1235.tif 250
output/1236.tif 251
output/1237.tif 252
output/1238.tif 253
output/1239.tif 254
output/1240.tif 255
output/1241.tif 256
output/1242.tif 257
output/1243.tif 258
output/1244.tif 259
output/1245.tif 260
output/1246.tif 261
output/1247.tif 262
output/1248.tif 263
output/1249.tif 264
output/1250.tif 265
output/1251.tif 266
output/1252.tif 267
output/1253.tif 268
output/1254.tif 269
output/1255.tif 270
output/1256.tif 271
output/1257.tif 272
output/1258.tif 273
output/1259.tif 274
output/1260.tif 275
output/1261.tif 276

Preface (p. XVI)

This book has grown out of undergraduate and postgraduate lecture courses given at the University of Hertfordshire and the University of Bergamo. Its pri- mary focus is on numerical methods for nonlinear optimization. Such methods can be applied to many practical problems in science, engineering and manage- ment: but, to provide a coherent secondary theme, the applications considered here are all drawn from financial mathematics. (This puts the book in good company since many classical texts in mathematics also dealt with commer- cial arithmetic.) In particular, the examples and case studies are concerned with portfolio selection and with time-series problems such as fitting trend- lines and trend-channels to market data.

The content is intended to be suitable for final-year undergraduate students in mathematics (or other subjects with a high mathematical or computational content) and exercises are provided at the end of most sections. However the book should also be useful for postgraduate students and for other researchers and practitioners who need a foundation for work involving development or application of optimization algorithms.

It is assumed that readers have an un- derstanding of the algebra of matrices and vectors and of the Taylor and Mean Value Theorems in several variables. Prior experience of using computational methods for problems such as solving systems of linear equations is also de- sirable, as is familiarity with iterative algorithms (e.g., Newton's method for nonlinear equations in one variable).

The approach adopted in this book is a blend of the practical and theoretical. A description and derivation is given for most of the currently popular methods for continuous nonlinear optimization. For each method, important conver- gence results are outlined (and we provide proofs when it seems instructive to do so). This theoretical material is complemented by numerical illustrations which give a flavour of how the methods perform in practice.

It is not always obvious where to draw the line between general descriptions of algorithms and the more subtle and detailed considerations relating to re- search issues. The particular themes and emphases in this book have grown out of the author's experience at the Numerical Optimization Centre (NOC). This was established in 1968 at the Hatfield College of Technology (predeces- sor of the University of Hertfordshire) as a centre for research in optimization techniques.

Since its foundation, the NOC has been engaged in algorithm de- velopment and consultancy work (mostly in the aerospace industry). The NOC staff has included, at various times, Laurence Dixon, Ed Hersom, Joanna Go- mulka, Sean McKeown and Zohair Maany who have all made contributions to the state-of-the-art in fields as diverse as quasi-Newton methods, sequential quadratic programming, nonlinear least-squares, global optimization, optimal control and automatic differentiation.

The computational results quoted in this book have been obtained using a Fortran90 module called SAMPO. This is based on the NOC's OPTIMA library - a suite of subroutines for different types of minimization problem. The name SAMPO serves as an acronym for Software And Methods for Portfolio Optimization. (However, it is also worth mentioning that The Sampo appears in Finnish mythology as a magical machine which grinds out endless supplies of corn, salt and gold.