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

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xx CONTENTS B.3.2 sparam.data file name . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 504 B.3.3 sparam.debug file name . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 505 B.3.4 sparam.feasrepair name prefix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 505 B.3.5 sparam.feasrepair name separator . . . . . . . . . . . . . . . . . . . . . . . . . . 505 B.3.6 sparam.feasrepair name wsumviol . . . . . . . . . . . . . . . . . . . . . . . . . . . 506 B.3.7 sparam.int sol file name . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 506 B.3.8 sparam.itr sol file name . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 506 B.3.9 sparam.mio debug string . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 507 B.3.10 sparam.param comment sign . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 507 B.3.11 sparam.param read file name . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 507 B.3.12 sparam.param write file name . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 508 B.3.13 sparam.read mps bou name . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 508 B.3.14 sparam.read mps obj name . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 508 B.3.15 sparam.read mps ran name . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 509 B.3.16 sparam.read mps rhs name . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 509 B.3.17 sparam.sensitivity file name . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 509 B.3.18 sparam.sensitivity res file name . . . . . . . . . . . . . . . . . . . . . . . . . . . . 510 B.3.19 sparam.sol filter xc low . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 510 B.3.20 sparam.sol filter xc upr . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 510 B.3.21 sparam.sol filter xx low . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 511 B.3.22 sparam.sol filter xx upr . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 511 B.3.23 sparam.stat file name . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 511 B.3.24 sparam.stat key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 512 B.3.25 sparam.stat name . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 512 B.3.26 sparam.write lp gen var name . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 512 C Response codes 515 D API constants 545 D.1 Constraint or variable access modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 545 D.2 Basis identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 545 D.3 Bound keys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 546 D.4 Specifies the branching direction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 546 D.5 Progress call-back codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 546 D.6 Types of convexity checks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 555 D.7 Compression types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 555 D.8 Cone types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 555 D.9 Data format types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 555 D.10 Double information items . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 556 D.11 Feasibility repair types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 561 D.12 License feature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 561 D.13 Integer information items. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 561 D.14 Information item types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 568 D.15 Hot-start type employed by the interior-point optimizers. . . . . . . . . . . . . . . . . 568 D.16 Input/output modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 569 D.17 Language selection constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 569
CONTENTS xxi D.18 Long integer information items. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 569 D.19 Mark . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 570 D.20 Continuous mixed-integer solution type . . . . . . . . . . . . . . . . . . . . . . . . . . . 571 D.21 Integer restrictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 571 D.22 Mixed-integer node selection types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 571 D.23 MPS file format type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 572 D.24 Message keys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 572 D.25 Cone types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 572 D.26 Objective sense types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 573 D.27 On/off . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 573 D.28 Optimizer types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 573 D.29 Ordering strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 574 D.30 Parameter type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 574 D.31 Presolve method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 575 D.32 Problem data items . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 575 D.33 Problem types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 575 D.34 Problem status keys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 576 D.35 Response code type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 577 D.36 Scaling type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 577 D.37 Scaling type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 577 D.38 Sensitivity types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 578 D.39 Degeneracy strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 578 D.40 Exploit duplicate columns. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 578 D.41 Hot-start type employed by the simplex optimizer . . . . . . . . . . . . . . . . . . . . . 578 D.42 Problem reformulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 579 D.43 Simplex selection strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 579 D.44 Solution items . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 580 D.45 Solution status keys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 580 D.46 Solution types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 581 D.47 Solve primal or dual form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 582 D.48 Status keys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 582 D.49 Starting point types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 582 D.50 Stream types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 583 D.51 Cone types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 583 D.52 Integer values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 583 D.53 Variable types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 584 D.54 XML writer output mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 584 E Troubleshooting 585 F Mosek file formats 587 F.1 The MPS file format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 587 F.1.1 MPS file structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 587 F.1.2 Integer variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 597 F.1.3 General limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 598 F.1.4 Interpretation of the MPS format . . . . . . . . . . . . . . . . . . . . . . . . . . . 598
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
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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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5.5. 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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Appendix C Response codes Response
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517 rescode.err con q not psd The q
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519 rescode.err global inv conic pr
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521 rescode.err inv markj Invalid v
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523 rescode.err invalid format type
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525 rescode.err license no server s
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527 rescode.err mio no optimizer No
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529 rescode.err name max len A name
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531 rescode.err numconlim Maximum n
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533 rescode.err qcon upper triangle
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535 rescode.err sym mat invalid col
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537 rescode.err user nlo func The u
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539 rescode.wrn ana almost int boun
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541 rescode.wrn mio infeasible fina
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543 rescode.wrn write discarded cfi
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Appendix D API constants D.1 Constr
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D.5. PROGRESS CALL-BACK CODES 547 c
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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
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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
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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
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D.46. SOLUTION TYPES 581 solsta.dua
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D.50. STREAM TYPES 583 startpointty
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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
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F.1. THE MPS FILE FORMAT 591 must b
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F.1. THE MPS FILE FORMAT 593 Constr
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F.1. THE MPS FILE FORMAT 595 v 1 is
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F.1. THE MPS FILE FORMAT 597 Please
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F.2. THE LP FILE FORMAT 599 minimiz
Page 623 and 624:
F.2. THE LP FILE FORMAT 601 st defi
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F.2. THE LP FILE FORMAT 603 bounds
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F.3. THE OPF FORMAT 605 iparam.writ
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F.3. THE OPF FORMAT 607 [tag "value
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F.3. THE OPF FORMAT 609 Note that a
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F.3. THE OPF FORMAT 611 F.3.2.3 Nam
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F.3. THE OPF FORMAT 613 [bounds] [b
Page 637 and 638:
F.4. THE TASK FORMAT 615 This can b
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F.7. THE SOLUTION FILE FORMAT 617 c
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Appendix G Problem analyzer example
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G.2. ARKI001 621 2 476 45.42 48.19
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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
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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
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INDEX 635 rescode.err sen bound inv
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The MOSEK Python optimizer API manual Version 7.0 (Revision 141)

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