The MOSEK Python optimizer API manual Version 7.0 (Revision 141)

More documents

Recommendations

Info

108 CHAPTER 8. A CASE STUDY 53 offsetx = 0 # Offset of variable x into the API variable. 54 offsets = n # Offset of variable x into the API variable. 55 offsett = n+1 # Offset of variable t into the API variable. 56 57 # x variables. 58 task.putclist(range(offsetx+0,offsetx+n),mu) 59 task.putaijlist(n*[0],range(offsetx+0,offsetx+n),n*[1.0]) 60 for j in range(0,n): 61 task.putaijlist(n*[1+j],range(offsetx+0,offsetx+n),GT[j]) 62 63 task.putvarboundlist(range(offsetx+0,offsetx+n),n*[mosek.boundkey.lo],n*[0.0],n*[inf]) 64 for j in range(0,n): 65 task.putvarname(offsetx+j,"x[%d]" % (1+j)) 66 67 # s variable. 68 task.putvarbound(offsets+0,mosek.boundkey.fr,gamma,gamma) 69 task.putvarname(offsets+0,"s") 70 71 # t variables. 72 task.putaijlist(range(1,n+1),range(offsett+0,offsett+n),n*[-1.0]) 73 task.putvarboundlist(range(offsett+0,offsett+n),n*[mosek.boundkey.fr],n*[-inf],n*[inf]) 74 for j in range(0,n): 75 task.putvarname(offsett+j,"t[%d]" % (1+j)) 76 77 task.appendcone(mosek.conetype.quad,0.0,[offsets] + range(offsett,offsett+n)) 78 task.putconename(0,"stddev") 79 80 task.putobjsense(mosek.objsense.maximize) 81 82 # Turn all log output off. 83 task.putintparam(mosek.iparam.log,0) 84 85 for alpha in alphas: 86 # Dump the problem to a human readable OPF file. 87 #task.writedata("dump.opf") 88 89 task.putcj(offsets+0,-alpha); 90 91 task.optimize() 92 93 # Display the solution summary for quick inspection of results. 94 # task.solutionsummary(mosek.streamtype.msg) 95 96 solsta = task.getsolsta(mosek.soltype.itr) 97 98 if solsta in [mosek.solsta.optimal, mosek.solsta.near optimal]: 99 expret = 0.0 100 x = zeros(n,float) 101 task.getxxslice(mosek.soltype.itr,offsetx+0,offsetx+n,x) 102 for j in range(0,n): 103 expret += mu[j]*x[j] 104 105 stddev = zeros(1,float) 106 task.getxxslice(mosek.soltype.itr,offsets+0,offsets+1,stddev) 107 108 print("\nExpected return %e for gamma %e" % (expret,stddev[0])), 109 else:
8.1. PORTFOLIO OPTIMIZATION 109 110 print("An error occurred when solving for alpha=%e\n" % alpha) 8.1.4 Improving the computational efficiency In practice it is often important to solve the portfolio problem in a short amount of time; this section it is discusses what can be done at the modelling stage to improve the computational efficiency. The computational cost is of course to some extent dependent on the number of constraints and variables in the optimization problem. However, in practice a more important factor is the number nonzeros used to represent the problem. Indeed it is often better to focus at the number of nonzeros in G (see (8.2)) and try to reduce that number by for instance changing the choice of G. In other words, if the computational efficiency should be improved then it is always good idea to start with focusing at the covariance matrix. As an example assume that Σ = D + V V T where D is positive definite diagonal matrix. Moreover, V is a matrix with n rows and p columns. Such a model for the covariance matrix is called a factor model and usually p is much smaller than n. In practice p tends be a small number say less than 100 independent of n. One possible choice for G is the Cholesky factorization of Σ which requires storage proportional to n(n + 1)/2. However, another choice is because then G T = [ D 1/2 V T ] GG T = D + V V T . This choice requires storage proportional to n + pn which is much less than for the Cholesky choice of G. Indeed assuming p is a constant then the difference in storage requirements is a factor of n. The example above exploits the so-called factor structure and demonstrates that an alternative choice of G may lead to a significant reduction in the amount of storage used to represent the problem. This will in most cases also lead to a significant reduction in the solution time. The lesson to be learned is that it is important to investigate how the covariance is formed. Given this knowledge it might be possible to make a special choice for G that helps reducing the storage requirements and enhance the computational efficiency. 8.1.5 Slippage cost The basic Markowitz portfolio model assumes that there are no costs associated with trading the assets and that the returns of the assets is independent of the amount traded. None of those assumptions are usually valid in practice. Therefore, a more realistic model is
Page 1 and 2:
The MOSEK Python optimizer API manu
Page 3 and 4:
Contents 1 Changes and new features
Page 5 and 6:
CONTENTS v 8 A case study 97 8.1 Po
Page 7 and 8:
CONTENTS vii 14.2.1 Caveats . . . .
Page 9 and 10:
CONTENTS ix A.2.70 Task.getdviolvar
Page 11 and 12:
CONTENTS xi A.2.162Task.isdouparnam
Page 13 and 14:
CONTENTS xiii A.2.254Task.readparam
Page 15 and 16:
CONTENTS xv B.1.45 dparam.mio near
Page 17 and 18:
CONTENTS xvii B.2.68 iparam.log sim
Page 19 and 20:
CONTENTS xix B.2.160iparam.sim refa
Page 21 and 22:
CONTENTS xxi D.18 Long integer info
Page 23 and 24:
Contact information Phone +45 3917
Page 25 and 26:
License agreement Before using the
Page 27 and 28:
Chapter 1 Changes and new features
Page 29 and 30:
1.4. API CHANGES 7 1.3.3 Mixed-inte
Page 31 and 32:
1.10. SUMMARY OF API CHANGES 9 •
Page 33 and 34:
Page 35 and 36:
Page 37 and 38:
Chapter 2 About this manual This ma
Page 39 and 40:
Chapter 3 Getting support and help
Page 41 and 42:
Chapter 4 Testing installation and
Page 43 and 44:
Chapter 5 Basic API tutorial In thi
Page 45 and 46:
5.1. THE BASICS 23 5 # 6 # Purpose:
Page 47 and 48:
5.2. LINEAR OPTIMIZATION 25 and the
Page 49 and 50:
5.2. LINEAR OPTIMIZATION 27 Load a
Page 51 and 52:
5.2. LINEAR OPTIMIZATION 29 Optimiz
Page 53 and 54:
5.2. LINEAR OPTIMIZATION 31 88 task
Page 55 and 56:
5.2. LINEAR OPTIMIZATION 33 51 mose
Page 57 and 58:
5.3. CONIC QUADRATIC OPTIMIZATION 3
Page 59 and 60:
5.3. CONIC QUADRATIC OPTIMIZATION 3
Page 61 and 62:
5.4. SEMIDEFINITE OPTIMIZATION 39 m
Page 63 and 64:
5.4. SEMIDEFINITE OPTIMIZATION 41 4
Page 65 and 66:
5.4. SEMIDEFINITE OPTIMIZATION 43 1
Page 67 and 68:
5.5. QUADRATIC OPTIMIZATION 45 with
Page 69 and 70:
5.5. QUADRATIC OPTIMIZATION 47 68 #
Page 71 and 72:
5.5. QUADRATIC OPTIMIZATION 49 5.5.
Page 73 and 74:
5.5. QUADRATIC OPTIMIZATION 51 81 a
Page 75 and 76:
5.6. THE SOLUTION SUMMARY 53 • Th
Page 77 and 78:
5.7. INTEGER OPTIMIZATION 55 21 # f
Page 79 and 80: 5.7. INTEGER OPTIMIZATION 57 137 sy
Page 81 and 82: 5.8. THE SOLUTION SUMMARY FOR MIXED
Page 83 and 84: 5.9. RESPONSE HANDLING 61 Note that
Page 85 and 86: 5.10. PROBLEM MODIFICATION AND REOP
Page 87 and 88: 5.10. PROBLEM MODIFICATION AND REOP
Page 89 and 90: 5.11. SOLUTION ANALYSIS 67 151 # Pu
Page 91 and 92: 5.13. CONVENTIONS EMPLOYED IN THE A
Page 99 and 100: Chapter 6 Nonlinear API tutorial Th
Page 101 and 102: 6.1. SEPARABLE CONVEX (SCOPT) INTER
Page 107 and 108: Chapter 7 Advanced API tutorial Thi
Page 109 and 110: 7.1. THE PROGRESS CALL-BACK 87 71 p
Page 111 and 112: 7.2. SOLVING LINEAR SYSTEMS INVOLVI
Page 119 and 120: Chapter 8 A case study 8.1 Portfoli
Page 121 and 122: 8.1. PORTFOLIO OPTIMIZATION 99 e T
Page 123 and 124: 8.1. PORTFOLIO OPTIMIZATION 101 is
Page 125 and 126: 8.1. PORTFOLIO OPTIMIZATION 103 15
Page 129: 8.1. PORTFOLIO OPTIMIZATION 107 8.1
Page 133 and 134: 8.1. PORTFOLIO OPTIMIZATION 111 z j
Page 135 and 136: 8.1. PORTFOLIO OPTIMIZATION 113 Var
Page 141 and 142: Chapter 9 Usage guidelines The purp
Page 143 and 144: 9.3. WRITING TASK DATA TO A FILE 12
Page 145 and 146: Chapter 10 Problem formulation and
Page 147 and 148: 10.1. LINEAR OPTIMIZATION 125 be a
Page 149 and 150: 10.2. CONIC QUADRATIC OPTIMIZATION
Page 151 and 152: 10.2. CONIC QUADRATIC OPTIMIZATION
Page 153 and 154: 10.3. SEMIDEFINITE OPTIMIZATION 131
Page 155 and 156: 10.4. QUADRATIC AND QUADRATICALLY C
Page 157 and 158: Chapter 11 The optimizers for conti
Page 159 and 160: 11.1. HOW AN OPTIMIZER WORKS 137 11
Page 161 and 162: 11.2. LINEAR OPTIMIZATION 139 11.2.
Page 163 and 164: 11.2. LINEAR OPTIMIZATION 141 Whene
Page 165 and 166: 11.2. LINEAR OPTIMIZATION 143 11.2.
Page 167 and 168: 11.2. LINEAR OPTIMIZATION 145 • R
Page 169 and 170: 11.5. NONLINEAR CONVEX OPTIMIZATION
Page 171 and 172: 11.6. SOLVING PROBLEMS IN PARALLEL
Page 177 and 178: Chapter 12 The optimizers for mixed
Page 179 and 180: 12.3. THE MIXED-INTEGER CONIC OPTIM
Page 181 and 182:
12.5. TERMINATION CRITERION 159 •
Page 183 and 184:
12.7. UNDERSTANDING SOLUTION QUALIT
Page 185 and 186:
Chapter 13 The analyzers 13.1 The p
Page 187 and 188:
13.1. THE PROBLEM ANALYZER 165 Cons
Page 189 and 190:
13.2. ANALYZING INFEASIBLE PROBLEMS
Page 191 and 192:
Page 193 and 194:
Page 195 and 196:
Page 197 and 198:
Page 199 and 200:
Chapter 14 Primal feasibility repai
Page 201 and 202:
14.2. AUTOMATIC REPAIR 179 One way
Page 203 and 204:
14.3. FEASIBILITY REPAIR IN MOSEK 1
Page 205 and 206:
14.3. FEASIBILITY REPAIR IN MOSEK 1
Page 207 and 208:
Chapter 15 Sensitivity analysis 15.
Page 209 and 210:
15.4. SENSITIVITY ANALYSIS FOR LINE
Page 211 and 212:
Page 213 and 214:
Page 215 and 216:
15.5. SENSITIVITY ANALYSIS FROM THE
Page 217 and 218:
15.6. SENSITIVITY ANALYSIS WITH THE
Page 219 and 220:
15.6. SENSITIVITY ANALYSIS WITH THE
Page 221 and 222:
Appendix A API reference This chapt
Page 223 and 224:
201 • Task.relaxprimal Obtain inf
Page 225 and 226:
A.1. EXCEPTIONS 203 • Task.putvar
Page 227 and 228:
A.2. CLASS TASK 205 Arguments which
Page 229 and 230:
A.2. CLASS TASK 207 See also • Ro
Page 231 and 232:
A.2. CLASS TASK 209 Description: Ap
Page 233 and 234:
A.2. CLASS TASK 211 Description: If
Page 235 and 236:
A.2. CLASS TASK 213 A.2.16 Task.com
Page 237 and 238:
A.2. CLASS TASK 215 subj : int[] In
Page 239 and 240:
A.2. CLASS TASK 217 firsti : int In
Page 241 and 242:
A.2. CLASS TASK 219 A.2.27 Task.get
Page 243 and 244:
A.2. CLASS TASK 221 valijkl : Descr
Page 245 and 246:
Page 247 and 248:
A.2. CLASS TASK 225 idx : long Inde
Page 249 and 250:
Page 251 and 252:
A.2. CLASS TASK 229 i : int Index o
Page 253 and 254:
Page 255 and 256:
A.2. CLASS TASK 233 conetype : cone
Page 257 and 258:
A.2. CLASS TASK 235 Description: Ob
Page 259 and 260:
A.2. CLASS TASK 237 sub : int[] Ind
Page 261 and 262:
Page 263 and 264:
A.2. CLASS TASK 241 Computes the vi
Page 265 and 266:
Page 267 and 268:
Page 269 and 270:
Page 271 and 272:
Page 273 and 274:
Page 275 and 276:
A.2. CLASS TASK 253 k : int Index o
Page 277 and 278:
A.2. CLASS TASK 255 A.2.103 Task.ge
Page 279 and 280:
A.2. CLASS TASK 257 normalize : int
Page 281 and 282:
A.2. CLASS TASK 259 Description: Le
Page 283 and 284:
A.2. CLASS TASK 261 max(l x j τ
Page 285 and 286:
Page 287 and 288:
A.2. CLASS TASK 265 last : int Last
Page 289 and 290:
Page 291 and 292:
A.2. CLASS TASK 269 Arguments snx :
Page 293 and 294:
A.2. CLASS TASK 271 slc : double[]
Page 295 and 296:
A.2. CLASS TASK 273 Arguments accmo
Page 297 and 298:
Page 299 and 300:
A.2. CLASS TASK 277 last : int Valu
Page 301 and 302:
A.2. CLASS TASK 279 subi : int[] Ro
Page 303 and 304:
Page 305 and 306:
A.2. CLASS TASK 283 Arguments taskn
Page 307 and 308:
Page 309 and 310:
A.2. CLASS TASK 287 vartype : varia
Page 311 and 312:
A.2. CLASS TASK 289 whichsol : solt
Page 313 and 314:
Page 315 and 316:
A.2. CLASS TASK 293 A.2.162 Task.is
Page 317 and 318:
A.2. CLASS TASK 295 whichstream : s
Page 319 and 320:
A.2. CLASS TASK 297 A.2.170 Task.pr
Page 321 and 322:
A.2. CLASS TASK 299 markj : mark Th
Page 323 and 324:
A.2. CLASS TASK 301 Prints a part o
Page 325 and 326:
A.2. CLASS TASK 303 A.2.175 Task.pu
Page 327 and 328:
A.2. CLASS TASK 305 j : int Index o
Page 329 and 330:
Page 331 and 332:
A.2. CLASS TASK 309 Description: Th
Page 333 and 334:
Page 335 and 336:
A.2. CLASS TASK 313 Changes the bou
Page 337 and 338:
A.2. CLASS TASK 315 Modifies one li
Page 339 and 340:
A.2. CLASS TASK 317 bkc : boundkey
Page 341 and 342:
A.2. CLASS TASK 319 Arguments j : i
Page 343 and 344:
A.2. CLASS TASK 321 parvalue : int
Page 345 and 346:
Page 347 and 348:
A.2. CLASS TASK 325 Sets a string p
Page 349 and 350:
A.2. CLASS TASK 327 Description: Re
Page 351 and 352:
A.2. CLASS TASK 329 qosubj : int[]
Page 353 and 354:
A.2. CLASS TASK 331 Sets the status
Page 355 and 356:
Page 357 and 358:
A.2. CLASS TASK 335 Arguments sux :
Page 359 and 360:
A.2. CLASS TASK 337 y : double[] Ve
Page 361 and 362:
Page 363 and 364:
A.2. CLASS TASK 341 last : int Last
Page 365 and 366:
A.2. CLASS TASK 343 See also • Ta
Page 367 and 368:
Page 369 and 370:
A.2. CLASS TASK 347 Description: Se
Page 371 and 372:
A.2. CLASS TASK 349 Sets a slice of
Page 373 and 374:
A.2. CLASS TASK 351 A.2.254 Task.re
Page 375 and 376:
A.2. CLASS TASK 353 wux : double[]
Page 377 and 378:
A.2. CLASS TASK 355 See also • Ta
Page 379 and 380:
A.2. CLASS TASK 357 isdef : int Is
Page 381 and 382:
A.2. CLASS TASK 359 A.2.269 Task.st
Page 383 and 384:
A.2. CLASS TASK 361 Description: Wr
Page 385 and 386:
A.3. CLASS ENV 363 A.2.278 Task.wri
Page 387 and 388:
A.3. CLASS ENV 365 Arguments code :
Page 389 and 390:
A.3. CLASS ENV 367 Arguments keepdl
Page 391 and 392:
A.4. CALLBACK FUNCTIONS AND RELATED
Page 393 and 394:
A.6. ALL FUNCTIONS BY NAME 371 Task
Page 395 and 396:
Page 397 and 398:
Page 399 and 400:
Page 401 and 402:
Page 403 and 404:
Page 405 and 406:
Page 407 and 408:
Page 409 and 410:
Page 411 and 412:
Appendix B Parameters Parameters gr
Page 413 and 414:
391 • iparam.log file. If turned
Page 415 and 416:
393 • dparam.intpnt nl tol rel st
Page 417 and 418:
395 • iparam.mio construct sol. C
Page 419 and 420:
397 • dparam.intpnt nl tol mu red
Page 421 and 422:
399 • iparam.mio mode. Turns on/o
Page 423 and 424:
401 • iparam.sim solve form. Cont
Page 425 and 426:
B.1. DPARAM: DOUBLE PARAMETERS 403
Page 427 and 428:
Page 429 and 430:
Page 431 and 432:
Page 433 and 434:
Page 435 and 436:
Page 437 and 438:
Page 439 and 440:
Page 441 and 442:
Page 443 and 444:
Page 445 and 446:
Page 447 and 448:
Page 449 and 450:
B.2. IPARAM: INTEGER PARAMETERS 427
Page 451 and 452:
Page 453 and 454:
Page 455 and 456:
Page 457 and 458:
Page 459 and 460:
Page 461 and 462:
Page 463 and 464:
Page 465 and 466:
Page 467 and 468:
Page 469 and 470:
Page 471 and 472:
Page 473 and 474:
Page 475 and 476:
Page 477 and 478:
Page 479 and 480:
Page 481 and 482:
Page 483 and 484:
Page 485 and 486:
Page 487 and 488:
Page 489 and 490:
Page 491 and 492:
Page 493 and 494:
Page 495 and 496:
Page 497 and 498:
Page 499 and 500:
Page 501 and 502:
Page 503 and 504:
Page 505 and 506:
Page 507 and 508:
Page 509 and 510:
Page 511 and 512:
Page 513 and 514:
Page 515 and 516:
Page 517 and 518:
Page 519 and 520:
Page 521 and 522:
Page 523 and 524:
Page 525 and 526:
Page 527 and 528:
B.3. SPARAM: STRING PARAMETER TYPES
Page 529 and 530:
Page 531 and 532:
Page 533 and 534:
Page 535 and 536:
Page 537 and 538:
Appendix C Response codes Response
Page 539 and 540:
517 rescode.err con q not psd The q
Page 541 and 542:
519 rescode.err global inv conic pr
Page 543 and 544:
521 rescode.err inv markj Invalid v
Page 545 and 546:
523 rescode.err invalid format type
Page 547 and 548:
525 rescode.err license no server s
Page 549 and 550:
527 rescode.err mio no optimizer No
Page 551 and 552:
529 rescode.err name max len A name
Page 553 and 554:
531 rescode.err numconlim Maximum n
Page 555 and 556:
533 rescode.err qcon upper triangle
Page 557 and 558:
535 rescode.err sym mat invalid col
Page 559 and 560:
537 rescode.err user nlo func The u
Page 561 and 562:
539 rescode.wrn ana almost int boun
Page 563 and 564:
541 rescode.wrn mio infeasible fina
Page 565 and 566:
543 rescode.wrn write discarded cfi
Page 567 and 568:
Appendix D API constants D.1 Constr
Page 569 and 570:
D.5. PROGRESS CALL-BACK CODES 547 c
Page 571 and 572:
Page 573 and 574:
Page 575 and 576:
Page 577 and 578:
D.6. TYPES OF CONVEXITY CHECKS. 555
Page 579 and 580:
D.10. DOUBLE INFORMATION ITEMS 557
Page 581 and 582:
D.10. DOUBLE INFORMATION ITEMS 559
Page 583 and 584:
D.11. FEASIBILITY REPAIR TYPES 561
Page 585 and 586:
D.13. INTEGER INFORMATION ITEMS. 56
Page 587 and 588:
Page 589 and 590:
Page 591 and 592:
D.16. INPUT/OUTPUT MODES 569 intpnt
Page 593 and 594:
D.20. CONTINUOUS MIXED-INTEGER SOLU
Page 595 and 596:
D.26. OBJECTIVE SENSE TYPES 573 D.2
Page 597 and 598:
D.31. PRESOLVE METHOD. 575 paramete
Page 599 and 600:
D.35. RESPONSE CODE TYPE 577 D.35 R
Page 601 and 602:
D.42. PROBLEM REFORMULATION. 579 si
Page 603 and 604:
D.46. SOLUTION TYPES 581 solsta.dua
Page 605 and 606:
D.50. STREAM TYPES 583 startpointty
Page 607 and 608:
Appendix E Troubleshooting When cre
Page 609 and 610:
Appendix F Mosek file formats MOSEK
Page 611 and 612:
F.1. THE MPS FILE FORMAT 589 Fields
Page 613 and 614:
F.1. THE MPS FILE FORMAT 591 must b
Page 615 and 616:
F.1. THE MPS FILE FORMAT 593 Constr
Page 617 and 618:
F.1. THE MPS FILE FORMAT 595 v 1 is
Page 619 and 620:
F.1. THE MPS FILE FORMAT 597 Please
Page 621 and 622:
F.2. THE LP FILE FORMAT 599 minimiz
Page 623 and 624:
F.2. THE LP FILE FORMAT 601 st defi
Page 625 and 626:
F.2. THE LP FILE FORMAT 603 bounds
Page 627 and 628:
F.3. THE OPF FORMAT 605 iparam.writ
Page 629 and 630:
F.3. THE OPF FORMAT 607 [tag "value
Page 631 and 632:
F.3. THE OPF FORMAT 609 Note that a
Page 633 and 634:
F.3. THE OPF FORMAT 611 F.3.2.3 Nam
Page 635 and 636:
F.3. THE OPF FORMAT 613 [bounds] [b
Page 637 and 638:
F.4. THE TASK FORMAT 615 This can b
Page 639 and 640:
F.7. THE SOLUTION FILE FORMAT 617 c
Page 641 and 642:
Appendix G Problem analyzer example
Page 643 and 644:
G.2. ARKI001 621 2 476 45.42 48.19
Page 645 and 646:
G.4. PROBLEM WITH BOTH LINEAR AND C
Page 647 and 648:
Bibliography [1] Chvátal, V.. Line
Page 649 and 650:
Index analyzenames (Task method), 2
Page 651 and 652:
INDEX 629 getpcni (Task method), 25
Page 653 and 654:
INDEX 631 putbarablocktriplet (Task
Page 655 and 656:
INDEX 633 rescode.err inv numj, 521
Page 657 and 658:
INDEX 635 rescode.err sen bound inv
show all

The MOSEK Python optimizer API manual Version 7.0 (Revision 141)

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?