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

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iv CONTENTS 5.3.1 Example: Conic quadratic optimization . . . . . . . . . . . . . . . . . . . . . . . 35 5.4 Semidefinite optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 5.4.1 Example: Semidefinite optimization . . . . . . . . . . . . . . . . . . . . . . . . . 39 5.5 Quadratic optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 5.5.1 Example: Quadratic objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 5.5.2 Example: Quadratic constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 5.6 The solution summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 5.7 Integer optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 5.7.1 Example: Mixed integer linear optimization . . . . . . . . . . . . . . . . . . . . . 54 5.7.2 Specifying an initial solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 5.7.3 Example: Specifying an integer solution . . . . . . . . . . . . . . . . . . . . . . . 57 5.8 The solution summary for mixed integer problems . . . . . . . . . . . . . . . . . . . . 59 5.9 Response handling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 5.10 Problem modification and reoptimization . . . . . . . . . . . . . . . . . . . . . . . . . . 62 5.10.1 Example: Production planning . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 5.10.2 Changing the A matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 5.10.3 Appending variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 5.10.4 Reoptimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 5.10.5 Appending constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 5.11 Solution analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 5.11.1 Retrieving solution quality information with the API . . . . . . . . . . . . . . . . 67 5.12 Efficiency considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 5.12.1 API overhead . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 5.13 Conventions employed in the API . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 5.13.1 Naming conventions for arguments . . . . . . . . . . . . . . . . . . . . . . . . . . 69 5.13.2 Vector formats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 5.13.3 Matrix formats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 5.13.4 Array objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 5.13.5 Typical problems using the Python API . . . . . . . . . . . . . . . . . . . . . . . 75 5.14 The license system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 5.14.1 Waiting for a free license . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 6 Nonlinear API tutorial 77 6.1 Separable convex (SCopt) interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 6.1.1 Adding separable terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 6.1.2 Example: Simple separable problem . . . . . . . . . . . . . . . . . . . . . . . . . 80 6.1.3 Ensuring convexity and differentiability . . . . . . . . . . . . . . . . . . . . . . . 82 6.1.4 SCopt Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 7 Advanced API tutorial 85 7.1 The progress call-back . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 7.1.1 Source code example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 7.2 Solving linear systems involving the basis matrix . . . . . . . . . . . . . . . . . . . . . 88 7.2.1 Identifying the basis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 7.2.2 An example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 7.2.3 Solving arbitrary linear systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

CONTENTS v 8 A case study 97 8.1 Portfolio optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 8.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 8.1.2 A basic portfolio optimization model . . . . . . . . . . . . . . . . . . . . . . . . . 98 8.1.3 The efficient frontier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 8.1.4 Improving the computational efficiency . . . . . . . . . . . . . . . . . . . . . . . 109 8.1.5 Slippage cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 9 Usage guidelines 119 9.1 Verifying the results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 9.1.1 Verifying primal feasibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 9.1.2 Verifying optimality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 9.2 Turn on logging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 9.3 Writing task data to a file . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 9.4 Important API limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 9.4.1 Thread safety . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 9.5 Bug reporting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 10 Problem formulation and solutions 123 10.1 Linear optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 10.1.1 Duality for linear optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 10.1.2 Infeasibility for linear optimization . . . . . . . . . . . . . . . . . . . . . . . . . . 126 10.2 Conic quadratic optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 10.2.1 Duality for conic quadratic optimization . . . . . . . . . . . . . . . . . . . . . . . 128 10.2.2 Infeasibility for conic quadratic optimization . . . . . . . . . . . . . . . . . . . . 129 10.3 Semidefinite optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 10.3.1 Duality for semidefinite optimization . . . . . . . . . . . . . . . . . . . . . . . . . 130 10.3.2 Infeasibility for semidefinite optimization . . . . . . . . . . . . . . . . . . . . . . 131 10.4 Quadratic and quadratically constrained optimization . . . . . . . . . . . . . . . . . . 132 10.4.1 Duality for quadratic and quadratically constrained optimization . . . . . . . . . 132 10.4.2 Infeasibility for quadratic and quadratically constrained optimization . . . . . . . 133 11 The optimizers for continuous problems 135 11.1 How an optimizer works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 11.1.1 Presolve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 11.1.2 Dualizer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 11.1.3 Scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 11.1.4 Using multiple threads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 11.2 Linear optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 11.2.1 Optimizer selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 11.2.2 The interior-point optimizer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 11.2.3 The simplex based optimizer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 11.2.4 The interior-point or the simplex optimizer? . . . . . . . . . . . . . . . . . . . . . 145 11.2.5 The primal or the dual simplex variant? . . . . . . . . . . . . . . . . . . . . . . . 145 11.3 Linear network optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 11.3.1 Network flow problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 11.4 Conic optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146

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Page 3: Contents 1 Changes and new features

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 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 and 130: 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 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 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 247 and 248: A.2. CLASS TASK 225 idx : long Inde


Page 251 and 252: A.2. CLASS TASK 229 i : int Index o


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 263 and 264: A.2. CLASS TASK 241 Computes the vi






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 287 and 288: A.2. CLASS TASK 265 last : int Last


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 299 and 300: A.2. CLASS TASK 277 last : int Valu

Page 301 and 302: A.2. CLASS TASK 279 subi : int[] Ro


Page 305 and 306: A.2. CLASS TASK 283 Arguments taskn


Page 309 and 310: A.2. CLASS TASK 287 vartype : varia

Page 311 and 312: A.2. CLASS TASK 289 whichsol : solt


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 331 and 332: A.2. CLASS TASK 309 Description: Th


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 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 357 and 358: A.2. CLASS TASK 335 Arguments sux :

Page 359 and 360: A.2. CLASS TASK 337 y : double[] Ve


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 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 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 449 and 450: B.2. IPARAM: INTEGER PARAMETERS 427







































Page 527 and 528: B.3. SPARAM: STRING PARAMETER TYPES





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 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 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

optimizer

dual

primal

mosek

obtains

optimization

corresponding

simplex

constraint

variable

python

manual

mosek.com

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