The MOSEK command line tool Version 7.0 (Revision 141)

More documents

Recommendations

Info

34 CHAPTER 5. THE OPTIMIZERS FOR CONTINUOUS PROBLEMS 5.1.1 Presolve Before an optimizer actually performs the optimization the problem is preprocessed using the so-called presolve. The purpose of the presolve is to • remove redundant constraints, • eliminate fixed variables, • remove linear dependencies, • substitute out (implied) free variables, and • reduce the size of the optimization problem in general. After the presolved problem has been optimized the solution is automatically postsolved so that the returned solution is valid for the original problem. Hence, the presolve is completely transparent. For further details about the presolve phase, please see [3], [4]. It is possible to fine-tune the behavior of the presolve or to turn it off entirely. If presolve consumes too much time or memory compared to the reduction in problem size gained it may be disabled. This is done by setting the parameter MSK IPAR PRESOLVE USE to MSK PRESOLVE MODE OFF. The two most time-consuming steps of the presolve are • the eliminator, and • the linear dependency check. Therefore, in some cases it is worthwhile to disable one or both of these. 5.1.1.1 Numerical issues in the presolve During the presolve the problem is reformulated so that it hopefully solves faster. However, in rare cases the presolved problem may be harder to solve then the original problem. The presolve may also be infeasible although the orinal problem is not. If it is suspected that presolved problem is much harder to solve than the original then it is suggested to first turn the eliminator off by setting the parameter MSK IPAR PRESOLVE ELIMINATOR USE. If that does not help, then trying to turn presolve off may help. Since all computations are done in finite prescision then the presolve employs some tolerances when concluding a variable is fixed or constraint is redundant. If it happens that MOSEK incorrectly concludes a problem is primal or dual infeasible, then it is worthwhile to try to reduce the parameters MSK DPAR PRESOLVE TOL X and MSK DPAR PRESOLVE TOL S. However, if actually help reducing the parameters then this should be taken as an indication of the problem is badly formulated.
5.1. HOW AN OPTIMIZER WORKS 35 5.1.1.2 Eliminator The purpose of the eliminator is to eliminate free and implied free variables from the problem using substitution. For instance, given the constraints y = ∑ x j , y, x ≥ 0, y is an implied free variable that can be substituted out of the problem, if deemed worthwhile. If the eliminator consumes too much time or memory compared to the reduction in problem size gained it may be disabled. This can be done with the parameter MSK IPAR PRESOLVE ELIMINATOR USE to MSK OFF. In rare cases the eliminator may cause that the problem becomes much hard to solve. 5.1.1.3 Linear dependency checker The purpose of the linear dependency check is to remove linear dependencies among the linear equalities. For instance, the three linear equalities x 1 + x 2 + x 3 = 1, x 1 + 0.5x 2 = 0.5, 0.5x 2 + x 3 = 0.5 contain exactly one linear dependency. This implies that one of the constraints can be dropped without changing the set of feasible solutions. Removing linear dependencies is in general a good idea since it reduces the size of the problem. Moreover, the linear dependencies are likely to introduce numerical problems in the optimization phase. It is best practise to build models without linear dependencies. If the linear dependencies are removed at the modeling stage, the linear dependency check can safely be disabled by setting the parameter MSK IPAR PRESOLVE LINDEP USE to MSK OFF. 5.1.2 Dualizer All linear, conic, and convex optimization problems have an equivalent dual problem associated with them. MOSEK has built-in heuristics to determine if it is most efficient to solve the primal or dual problem. The form (primal or dual) solved is displayed in the MOSEK log. Should the internal heuristics not choose the most efficient form of the problem it may be worthwhile to set the dualizer manually by setting the parameters: • MSK IPAR INTPNT SOLVE FORM: In case of the interior-point optimizer. • MSK IPAR SIM SOLVE FORM: In case of the simplex optimizer. Note that currently only linear problems may be dualized.
Page 1 and 2: The MOSEK command line tool. Versio
Page 3 and 4: Contents 1 Changes and new features
Page 5 and 6: CONTENTS v 6.5 Termination criterio
Page 7 and 8: CONTENTS vii 9.1.56 MSK DPAR NONCON
Page 9 and 10: CONTENTS ix 9.2.79 MSK IPAR MIO FEA
Page 11 and 12: CONTENTS xi 9.2.171 MSK IPAR SOL RE
Page 13 and 14: CONTENTS xiii 11.29 Ordering strate
Page 15 and 16: CONTENTS xv 18.2 arki001 . . . . .
Page 17 and 18: Contact information Phone +45 3917
Page 19 and 20: License agreement Before using the
Page 21 and 22: Chapter 1 Changes and new features
Page 23 and 24: 1.4. OPTIMIZATION TOOLBOX FOR MATLA
Page 25 and 26: Chapter 2 What is MOSEK MOSEK is a
Page 27 and 28: Chapter 3 MOSEK and AMPL AMPL is a
Page 29 and 30: 3.6. CONSTRAINT AND VARIABLE NAMES
Page 31 and 32: 3.8. HOT-START 15 Linear dependency
Page 33 and 34: 3.10. SENSITIVITY ANALYSIS 17 • .
Page 35 and 36: Chapter 4 Problem formulation and s
Page 37 and 38: 4.1. LINEAR OPTIMIZATION 21 be a pr
Page 39 and 40: 4.2. CONIC QUADRATIC OPTIMIZATION 2
Page 41 and 42: 4.2. CONIC QUADRATIC OPTIMIZATION 2
Page 43 and 44: 4.3. SEMIDEFINITE OPTIMIZATION 27 4
Page 45 and 46: 4.5. GENERAL CONVEX OPTIMIZATION 29
Page 47 and 48: 4.5. GENERAL CONVEX OPTIMIZATION 31
Page 49: Chapter 5 The optimizers for contin
Page 53 and 54: 5.2. LINEAR OPTIMIZATION 37 5.2.2 T
Page 55 and 56: 5.2. LINEAR OPTIMIZATION 39 Wheneve
Page 57 and 58: 5.2. LINEAR OPTIMIZATION 41 5.2.2.3
Page 59 and 60: 5.2. LINEAR OPTIMIZATION 43 • Rai
Page 61 and 62: 5.5. NONLINEAR CONVEX OPTIMIZATION
Page 63 and 64: 5.6. SOLVING PROBLEMS IN PARALLEL 4
Page 65 and 66: Chapter 6 The optimizers for mixed-
Page 67 and 68: 6.3. THE MIXED-INTEGER CONIC OPTIMI
Page 69 and 70: 6.5. TERMINATION CRITERION 53 The f
Page 71 and 72: 6.7. UNDERSTANDING SOLUTION QUALITY
Page 73 and 74: Chapter 7 The analyzers 7.1 The pro
Page 75 and 76: 7.1. THE PROBLEM ANALYZER 59 Constr
Page 77 and 78: 7.2. ANALYZING INFEASIBLE PROBLEMS
Page 87 and 88: Chapter 8 Sensitivity analysis 8.1
Page 89 and 90: 8.4. SENSITIVITY ANALYSIS FOR LINEA
Page 91 and 92: 8.5. SENSITIVITY ANALYSIS WITH THE
Page 93 and 94: 8.5. SENSITIVITY ANALYSIS WITH THE
Page 95 and 96: Chapter 9 Parameters Parameters gro
Page 97 and 98: 81 • MSK SPAR ITR SOL FILE NAME.
Page 99 and 100: 83 • MSK DPAR INTPNT NL TOL REL G
Page 101 and 102:
85 • MSK IPAR LOG MIO. Controls t
Page 103 and 104:
87 • MSK DPAR INTPNT NL MERIT BAL
Page 105 and 106:
89 • MSK IPAR INFEAS PREFER PRIMA
Page 107 and 108:
91 • MSK IPAR SIM SAVE LU. Contro
Page 109 and 110:
9.1. MSKDPARAME: DOUBLE PARAMETERS
Page 111 and 112:
Page 113 and 114:
Page 115 and 116:
Page 117 and 118:
Page 119 and 120:
Page 121 and 122:
Page 123 and 124:
Page 125 and 126:
Page 127 and 128:
Page 129 and 130:
Page 131 and 132:
Page 133 and 134:
9.2. MSKIPARAME: INTEGER PARAMETERS
Page 135 and 136:
Page 137 and 138:
Page 139 and 140:
Page 141 and 142:
Page 143 and 144:
Page 145 and 146:
Page 147 and 148:
Page 149 and 150:
Page 151 and 152:
Page 153 and 154:
Page 155 and 156:
Page 157 and 158:
Page 159 and 160:
Page 161 and 162:
Page 163 and 164:
Page 165 and 166:
Page 167 and 168:
Page 169 and 170:
Page 171 and 172:
Page 173 and 174:
Page 175 and 176:
Page 177 and 178:
Page 179 and 180:
Page 181 and 182:
Page 183 and 184:
Page 185 and 186:
Page 187 and 188:
Page 189 and 190:
Page 191 and 192:
Page 193 and 194:
Page 195 and 196:
Page 197 and 198:
Page 199 and 200:
Page 201 and 202:
Page 203 and 204:
Page 205 and 206:
Page 207 and 208:
Page 209 and 210:
Page 211 and 212:
9.3. MSKSPARAME: STRING PARAMETER T
Page 213 and 214:
Page 215 and 216:
Page 217 and 218:
Page 219 and 220:
Chapter 10 Response codes Response
Page 221 and 222:
205 MSK RES ERR CON Q NOT PSD The q
Page 223 and 224:
207 MSK RES ERR GLOBAL INV CONIC PR
Page 225 and 226:
209 MSK RES ERR INV MARKJ Invalid v
Page 227 and 228:
211 MSK RES ERR INVALID FORMAT TYPE
Page 229 and 230:
213 MSK RES ERR LICENSE NO SERVER S
Page 231 and 232:
215 MSK RES ERR MIO NO OPTIMIZER No
Page 233 and 234:
217 MSK RES ERR NAME MAX LEN A name
Page 235 and 236:
219 MSK RES ERR NUMCONLIM Maximum n
Page 237 and 238:
221 MSK RES ERR QCON UPPER TRIANGLE
Page 239 and 240:
223 MSK RES ERR SYM MAT INVALID COL
Page 241 and 242:
225 MSK RES ERR USER NLO FUNC The u
Page 243 and 244:
227 MSK RES WRN ANA ALMOST INT BOUN
Page 245 and 246:
229 MSK RES WRN MIO INFEASIBLE FINA
Page 247 and 248:
231 MSK RES WRN WRITE DISCARDED CFI
Page 249 and 250:
Chapter 11 API constants 11.1 Const
Page 251 and 252:
11.5. PROGRESS CALL-BACK CODES 235
Page 253 and 254:
Page 255 and 256:
Page 257 and 258:
Page 259 and 260:
11.6. TYPES OF CONVEXITY CHECKS. 24
Page 261 and 262:
11.10. DOUBLE INFORMATION ITEMS 245
Page 263 and 264:
11.10. DOUBLE INFORMATION ITEMS 247
Page 265 and 266:
11.11. FEASIBILITY REPAIR TYPES 249
Page 267 and 268:
11.13. INTEGER INFORMATION ITEMS. 2
Page 269 and 270:
Page 271 and 272:
Page 273 and 274:
11.17. LANGUAGE SELECTION CONSTANTS
Page 275 and 276:
11.22. MIXED-INTEGER NODE SELECTION
Page 277 and 278:
11.29. ORDERING STRATEGIES 261 MSK
Page 279 and 280:
11.34. PROBLEM STATUS KEYS 263 MSK
Page 281 and 282:
11.38. SENSITIVITY TYPES 265 MSK SC
Page 283 and 284:
11.44. SOLUTION ITEMS 267 MSK SIM S
Page 285 and 286:
11.46. SOLUTION TYPES 269 11.46 Sol
Page 287 and 288:
11.52. INTEGER VALUES 271 11.52 Int
Page 289 and 290:
Chapter 12 MOSEK Command line tool
Page 291 and 292:
12.3. THE PARAMETER FILE 275 -min F
Page 293 and 294:
Chapter 13 The MPS file format MOSE
Page 295 and 296:
13.1. MPS FILE STRUCTURE 279 Extens
Page 297 and 298:
13.1. MPS FILE STRUCTURE 281 [vname
Page 299 and 300:
13.1. MPS FILE STRUCTURE 283 Field
Page 301 and 302:
13.1. MPS FILE STRUCTURE 285 Next d
Page 303 and 304:
13.2. INTEGER VARIABLES 287 13.2 In
Page 305 and 306:
Chapter 14 The LP file format MOSEK
Page 307 and 308:
14.1. THE SECTIONS 291 x1 * x2 Ther
Page 309 and 310:
14.2. LP FORMAT PECULIARITIES 293 1
Page 311 and 312:
14.3. THE STRICT LP FORMAT 295 MSK
Page 313 and 314:
Chapter 15 The OPF format The Optim
Page 315 and 316:
15.2. THE FILE FORMAT 299 [con ’c
Page 317 and 318:
15.2. THE FILE FORMAT 301 - ‘NEAR
Page 319 and 320:
15.4. WRITING OPF FILES FROM MOSEK
Page 321 and 322:
15.5. EXAMPLES 305 [/hints] [variab
Page 323 and 324:
15.5. EXAMPLES 307 x1 x2 [/integer]
Page 325 and 326:
Chapter 16 The XML (OSiL) format MO
Page 327 and 328:
Chapter 17 The solution file format
Page 329 and 330:
17.2. THE INTEGER SOLUTION FILE 313
Page 331 and 332:
Chapter 18 Problem analyzer example
Page 333 and 334:
18.2. ARKI001 317 2 476 45.42 48.19
Page 335 and 336:
18.4. PROBLEM WITH BOTH LINEAR AND
Page 337 and 338:
Bibliography [1] R. Fourer and D. M
Page 339 and 340:
Index AMPL outlev, 13 wantsol, 13 a
Page 341 and 342:
INDEX 325 MSK RES ERR FEASREPAIR IN
Page 343 and 344:
INDEX 327 MSK RES ERR MPS NULL VAR
Page 345 and 346:
INDEX 329 MSK RES TRM MAX TIME, 226
show all

The MOSEK command line tool Version 7.0 (Revision 141)

Create successful ePaper yourself

Delete template?

Save as template?