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

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xiv CONTENTS B Parameters 389 B.1 dparam: Double parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403 B.1.1 dparam.ana sol infeas tol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403 B.1.2 dparam.basis rel tol s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403 B.1.3 dparam.basis tol s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403 B.1.4 dparam.basis tol x . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404 B.1.5 dparam.check convexity rel tol . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404 B.1.6 dparam.data tol aij . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404 B.1.7 dparam.data tol aij huge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405 B.1.8 dparam.data tol aij large . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405 B.1.9 dparam.data tol bound inf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405 B.1.10 dparam.data tol bound wrn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 406 B.1.11 dparam.data tol c huge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 406 B.1.12 dparam.data tol cj large . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 406 B.1.13 dparam.data tol qij . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407 B.1.14 dparam.data tol x . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407 B.1.15 dparam.feasrepair tol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407 B.1.16 dparam.intpnt co tol dfeas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 408 B.1.17 dparam.intpnt co tol infeas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 408 B.1.18 dparam.intpnt co tol mu red . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 409 B.1.19 dparam.intpnt co tol near rel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 409 B.1.20 dparam.intpnt co tol pfeas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 409 B.1.21 dparam.intpnt co tol rel gap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 410 B.1.22 dparam.intpnt nl merit bal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 410 B.1.23 dparam.intpnt nl tol dfeas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 410 B.1.24 dparam.intpnt nl tol mu red . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 411 B.1.25 dparam.intpnt nl tol near rel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 411 B.1.26 dparam.intpnt nl tol pfeas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 411 B.1.27 dparam.intpnt nl tol rel gap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412 B.1.28 dparam.intpnt nl tol rel step . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412 B.1.29 dparam.intpnt tol dfeas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412 B.1.30 dparam.intpnt tol dsafe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413 B.1.31 dparam.intpnt tol infeas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413 B.1.32 dparam.intpnt tol mu red . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413 B.1.33 dparam.intpnt tol path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414 B.1.34 dparam.intpnt tol pfeas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414 B.1.35 dparam.intpnt tol psafe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414 B.1.36 dparam.intpnt tol rel gap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415 B.1.37 dparam.intpnt tol rel step . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415 B.1.38 dparam.intpnt tol step size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415 B.1.39 dparam.lower obj cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 416 B.1.40 dparam.lower obj cut finite trh . . . . . . . . . . . . . . . . . . . . . . . . . . . . 416 B.1.41 dparam.mio disable term time . . . . . . . . . . . . . . . . . . . . . . . . . . . . 417 B.1.42 dparam.mio heuristic time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 417 B.1.43 dparam.mio max time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 418 B.1.44 dparam.mio max time aprx opt . . . . . . . . . . . . . . . . . . . . . . . . . . . . 418
CONTENTS xv B.1.45 dparam.mio near tol abs gap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 418 B.1.46 dparam.mio near tol rel gap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419 B.1.47 dparam.mio rel add cut limited . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419 B.1.48 dparam.mio rel gap const . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 420 B.1.49 dparam.mio tol abs gap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 420 B.1.50 dparam.mio tol abs relax int . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 420 B.1.51 dparam.mio tol feas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 421 B.1.52 dparam.mio tol rel dual bound improvement . . . . . . . . . . . . . . . . . . . . 421 B.1.53 dparam.mio tol rel gap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 421 B.1.54 dparam.mio tol rel relax int . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422 B.1.55 dparam.mio tol x . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422 B.1.56 dparam.nonconvex tol feas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422 B.1.57 dparam.nonconvex tol opt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423 B.1.58 dparam.optimizer max time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423 B.1.59 dparam.presolve tol abs lindep . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423 B.1.60 dparam.presolve tol aij . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 424 B.1.61 dparam.presolve tol rel lindep . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 424 B.1.62 dparam.presolve tol s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 424 B.1.63 dparam.presolve tol x . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425 B.1.64 dparam.qcqo reformulate rel drop tol . . . . . . . . . . . . . . . . . . . . . . . . 425 B.1.65 dparam.sim lu tol rel piv . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425 B.1.66 dparam.simplex abs tol piv . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 426 B.1.67 dparam.upper obj cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 426 B.1.68 dparam.upper obj cut finite trh . . . . . . . . . . . . . . . . . . . . . . . . . . . . 426 B.2 iparam: Integer parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 427 B.2.1 iparam.alloc add qnz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 427 B.2.2 iparam.ana sol basis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 427 B.2.3 iparam.ana sol print violated . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 427 B.2.4 iparam.auto sort a before opt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 428 B.2.5 iparam.auto update sol info . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 428 B.2.6 iparam.basis solve use plus one . . . . . . . . . . . . . . . . . . . . . . . . . . . . 429 B.2.7 iparam.bi clean optimizer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 429 B.2.8 iparam.bi ignore max iter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 430 B.2.9 iparam.bi ignore num error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 430 B.2.10 iparam.bi max iterations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 430 B.2.11 iparam.cache license . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431 B.2.12 iparam.check convexity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431 B.2.13 iparam.compress statfile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 432 B.2.14 iparam.concurrent num optimizers . . . . . . . . . . . . . . . . . . . . . . . . . . 432 B.2.15 iparam.concurrent priority dual simplex . . . . . . . . . . . . . . . . . . . . . . . 432 B.2.16 iparam.concurrent priority free simplex . . . . . . . . . . . . . . . . . . . . . . . 433 B.2.17 iparam.concurrent priority intpnt . . . . . . . . . . . . . . . . . . . . . . . . . . . 433 B.2.18 iparam.concurrent priority primal simplex . . . . . . . . . . . . . . . . . . . . . . 433 B.2.19 iparam.feasrepair optimize . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434 B.2.20 iparam.infeas generic names . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434 B.2.21 iparam.infeas prefer primal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434
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 . . . .
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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
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5.4. SEMIDEFINITE OPTIMIZATION 43 1
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5.5. QUADRATIC OPTIMIZATION 45 with
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5.5. QUADRATIC OPTIMIZATION 47 68 #
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5.5. QUADRATIC OPTIMIZATION 49 5.5.
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5.5. QUADRATIC OPTIMIZATION 51 81 a
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5.6. THE SOLUTION SUMMARY 53 • Th
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5.7. INTEGER OPTIMIZATION 55 21 # f
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5.7. INTEGER OPTIMIZATION 57 137 sy
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5.8. THE SOLUTION SUMMARY FOR MIXED
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5.9. RESPONSE HANDLING 61 Note that
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5.10. PROBLEM MODIFICATION AND REOP
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5.10. PROBLEM MODIFICATION AND REOP
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5.11. SOLUTION ANALYSIS 67 151 # Pu
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5.13. CONVENTIONS EMPLOYED IN THE A
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Chapter 6 Nonlinear API tutorial Th
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6.1. SEPARABLE CONVEX (SCOPT) INTER
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Chapter 7 Advanced API tutorial Thi
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7.1. THE PROGRESS CALL-BACK 87 71 p
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7.2. SOLVING LINEAR SYSTEMS INVOLVI
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Chapter 8 A case study 8.1 Portfoli
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8.1. PORTFOLIO OPTIMIZATION 99 e T
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8.1. PORTFOLIO OPTIMIZATION 101 is
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8.1. PORTFOLIO OPTIMIZATION 103 15
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8.1. PORTFOLIO OPTIMIZATION 107 8.1
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8.1. PORTFOLIO OPTIMIZATION 111 z j
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8.1. PORTFOLIO OPTIMIZATION 113 Var
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Chapter 9 Usage guidelines The purp
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9.3. WRITING TASK DATA TO A FILE 12
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Chapter 10 Problem formulation and
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10.1. LINEAR OPTIMIZATION 125 be a
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10.2. CONIC QUADRATIC OPTIMIZATION
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10.2. CONIC QUADRATIC OPTIMIZATION
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10.3. SEMIDEFINITE OPTIMIZATION 131
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10.4. QUADRATIC AND QUADRATICALLY C
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Chapter 11 The optimizers for conti
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11.1. HOW AN OPTIMIZER WORKS 137 11
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11.2. LINEAR OPTIMIZATION 139 11.2.
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11.2. LINEAR OPTIMIZATION 141 Whene
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11.2. LINEAR OPTIMIZATION 143 11.2.
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11.2. LINEAR OPTIMIZATION 145 • R
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11.5. NONLINEAR CONVEX OPTIMIZATION
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11.6. SOLVING PROBLEMS IN PARALLEL
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Chapter 12 The optimizers for mixed
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12.3. THE MIXED-INTEGER CONIC OPTIM
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12.5. TERMINATION CRITERION 159 •
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12.7. UNDERSTANDING SOLUTION QUALIT
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Chapter 13 The analyzers 13.1 The p
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13.1. THE PROBLEM ANALYZER 165 Cons
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13.2. ANALYZING INFEASIBLE PROBLEMS
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Chapter 14 Primal feasibility repai
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14.2. AUTOMATIC REPAIR 179 One way
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14.3. FEASIBILITY REPAIR IN MOSEK 1
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14.3. FEASIBILITY REPAIR IN MOSEK 1
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Chapter 15 Sensitivity analysis 15.
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15.4. SENSITIVITY ANALYSIS FOR LINE
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15.5. SENSITIVITY ANALYSIS FROM THE
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15.6. SENSITIVITY ANALYSIS WITH THE
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15.6. SENSITIVITY ANALYSIS WITH THE
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Appendix A API reference This chapt
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201 • Task.relaxprimal Obtain inf
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A.1. EXCEPTIONS 203 • Task.putvar
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A.2. CLASS TASK 205 Arguments which
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A.2. CLASS TASK 207 See also • Ro
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A.2. CLASS TASK 209 Description: Ap
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A.2. CLASS TASK 211 Description: If
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A.2. CLASS TASK 213 A.2.16 Task.com
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A.2. CLASS TASK 215 subj : int[] In
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A.2. CLASS TASK 217 firsti : int In
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A.2. CLASS TASK 219 A.2.27 Task.get
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A.2. CLASS TASK 221 valijkl : Descr
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A.2. CLASS TASK 225 idx : long Inde
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A.2. CLASS TASK 229 i : int Index o
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A.2. CLASS TASK 233 conetype : cone
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A.2. CLASS TASK 235 Description: Ob
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A.2. CLASS TASK 237 sub : int[] Ind
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A.2. CLASS TASK 241 Computes the vi
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A.2. CLASS TASK 253 k : int Index o
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A.2. CLASS TASK 255 A.2.103 Task.ge
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A.2. CLASS TASK 257 normalize : int
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A.2. CLASS TASK 259 Description: Le
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A.2. CLASS TASK 261 max(l x j τ
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A.2. CLASS TASK 265 last : int Last
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A.2. CLASS TASK 269 Arguments snx :
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A.2. CLASS TASK 271 slc : double[]
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A.2. CLASS TASK 273 Arguments accmo
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A.2. CLASS TASK 277 last : int Valu
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A.2. CLASS TASK 279 subi : int[] Ro
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A.2. CLASS TASK 283 Arguments taskn
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A.2. CLASS TASK 287 vartype : varia
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A.2. CLASS TASK 289 whichsol : solt
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A.2. CLASS TASK 293 A.2.162 Task.is
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A.2. CLASS TASK 295 whichstream : s
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A.2. CLASS TASK 297 A.2.170 Task.pr
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A.2. CLASS TASK 299 markj : mark Th
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A.2. CLASS TASK 301 Prints a part o
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A.2. CLASS TASK 303 A.2.175 Task.pu
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A.2. CLASS TASK 305 j : int Index o
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A.2. CLASS TASK 309 Description: Th
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A.2. CLASS TASK 313 Changes the bou
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A.2. CLASS TASK 315 Modifies one li
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A.2. CLASS TASK 317 bkc : boundkey
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A.2. CLASS TASK 319 Arguments j : i
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A.2. CLASS TASK 321 parvalue : int
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A.2. CLASS TASK 325 Sets a string p
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A.2. CLASS TASK 327 Description: Re
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A.2. CLASS TASK 329 qosubj : int[]
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A.2. CLASS TASK 331 Sets the status
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A.2. CLASS TASK 335 Arguments sux :
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A.2. CLASS TASK 337 y : double[] Ve
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A.2. CLASS TASK 341 last : int Last
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A.2. CLASS TASK 343 See also • Ta
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A.2. CLASS TASK 347 Description: Se
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A.2. CLASS TASK 349 Sets a slice of
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A.2. CLASS TASK 351 A.2.254 Task.re
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A.2. CLASS TASK 353 wux : double[]
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A.2. CLASS TASK 355 See also • Ta
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A.2. CLASS TASK 357 isdef : int Is
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A.2. CLASS TASK 359 A.2.269 Task.st
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A.2. CLASS TASK 361 Description: Wr
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A.3. CLASS ENV 363 A.2.278 Task.wri
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A.3. CLASS ENV 365 Arguments code :
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A.3. CLASS ENV 367 Arguments keepdl
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A.4. CALLBACK FUNCTIONS AND RELATED
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A.6. ALL FUNCTIONS BY NAME 371 Task
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Appendix B Parameters Parameters gr
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391 • iparam.log file. If turned
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393 • dparam.intpnt nl tol rel st
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395 • iparam.mio construct sol. C
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397 • dparam.intpnt nl tol mu red
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399 • iparam.mio mode. Turns on/o
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401 • iparam.sim solve form. Cont
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B.1. DPARAM: DOUBLE PARAMETERS 403
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B.2. IPARAM: INTEGER PARAMETERS 427
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B.3. SPARAM: STRING PARAMETER TYPES
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Page 537 and 538:
Appendix C Response codes Response
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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
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D.5. PROGRESS CALL-BACK CODES 547 c
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Page 577 and 578:
D.6. TYPES OF CONVEXITY CHECKS. 555
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D.10. DOUBLE INFORMATION ITEMS 557
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D.10. DOUBLE INFORMATION ITEMS 559
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D.11. FEASIBILITY REPAIR TYPES 561
Page 585 and 586:
D.13. INTEGER INFORMATION ITEMS. 56
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D.16. INPUT/OUTPUT MODES 569 intpnt
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D.20. CONTINUOUS MIXED-INTEGER SOLU
Page 595 and 596:
D.26. OBJECTIVE SENSE TYPES 573 D.2
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D.31. PRESOLVE METHOD. 575 paramete
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D.35. RESPONSE CODE TYPE 577 D.35 R
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D.42. PROBLEM REFORMULATION. 579 si
Page 603 and 604:
D.46. SOLUTION TYPES 581 solsta.dua
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D.50. STREAM TYPES 583 startpointty
Page 607 and 608:
Appendix E Troubleshooting When cre
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Appendix F Mosek file formats MOSEK
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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
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Index analyzenames (Task method), 2
Page 651 and 652:
INDEX 629 getpcni (Task method), 25
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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
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