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

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x CONTENTS A.2.116Task.getqobj64() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262 A.2.117Task.getqobjij() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263 A.2.118Task.getreducedcosts() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263 A.2.119Task.getskc() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264 A.2.120Task.getskcslice() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264 A.2.121Task.getskx() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265 A.2.122Task.getskxslice() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265 A.2.123Task.getslc() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266 A.2.124Task.getslcslice() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267 A.2.125Task.getslx() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267 A.2.126Task.getslxslice() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268 A.2.127Task.getsnx() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268 A.2.128Task.getsnxslice() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269 A.2.129Task.getsolsta() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270 A.2.130Task.getsolution() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270 A.2.131Task.getsolutioni() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272 A.2.132Task.getsolutioninf() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 A.2.133Task.getsolutioninfo() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275 A.2.134Task.getsolutionslice() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276 A.2.135Task.getsparsesymmat() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278 A.2.136Task.getstrparam() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279 A.2.137Task.getstrparamlen() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279 A.2.138Task.getsuc() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280 A.2.139Task.getsucslice() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280 A.2.140Task.getsux() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281 A.2.<strong>141</strong>Task.getsuxslice() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281 A.2.142Task.getsymmatinfo() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282 A.2.143Task.gettaskname() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282 A.2.144Task.gettasknamelen() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283 A.2.145Task.getvarbound() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283 A.2.146Task.getvarboundslice() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284 A.2.147Task.getvarbranchdir() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284 A.2.148Task.getvarbranchpri() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285 A.2.149Task.getvarname() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285 A.2.150Task.getvarnameindex() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285 A.2.151Task.getvarnamelen() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286 A.2.152Task.getvartype() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286 A.2.153Task.getvartypelist() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287 A.2.154Task.getxc() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287 A.2.155Task.getxcslice() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288 A.2.156Task.getxx() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288 A.2.157Task.getxxslice() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289 A.2.158Task.gety() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290 A.2.159Task.getyslice() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290 A.2.160Task.initbasissolve() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291 A.2.161Task.inputdata() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291
CONTENTS xi A.2.162Task.isdouparname() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293 A.2.163Task.isintparname() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293 A.2.164Task.isstrparname() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293 A.2.165Task.linkfiletostream() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294 A.2.166Task.onesolutionsummary() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294 A.2.167Task.optimize() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295 A.2.168Task.optimizeconcurrent() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295 A.2.169Task.<strong>optimizer</strong>summary() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296 A.2.170Task.primalrepair() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297 A.2.171Task.primalsensitivity() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 298 A.2.172Task.printdata() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300 A.2.173Task.printparam() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302 A.2.174Task.putacol() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302 A.2.175Task.putacollist() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303 A.2.176Task.putacolslice() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303 A.2.177Task.putaij() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304 A.2.178Task.putaijlist() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305 A.2.179Task.putarow() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306 A.2.180Task.putarowlist() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307 A.2.181Task.putbarablocktriplet() . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307 A.2.182Task.putbaraij() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308 A.2.183Task.putbarcblocktriplet() . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309 A.2.184Task.putbarcj() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309 A.2.185Task.putbarsj() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310 A.2.186Task.putbarvarname() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311 A.2.187Task.putbarxj() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311 A.2.188Task.putbound() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312 A.2.189Task.putboundlist() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312 A.2.190Task.putboundslice() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313 A.2.191Task.putcfix() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314 A.2.192Task.putcj() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314 A.2.193Task.putclist() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315 A.2.194Task.putconbound() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316 A.2.195Task.putconboundlist() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316 A.2.196Task.putconboundslice() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317 A.2.197Task.putcone() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318 A.2.198Task.putconename() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318 A.2.199Task.putconname() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319 A.2.200Task.putcslice() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319 A.2.201Task.putdouparam() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320 A.2.202Task.putintparam() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320 A.2.203Task.putmaxnumanz() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321 A.2.204Task.putmaxnumbarvar() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321 A.2.205Task.putmaxnumcon() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322 A.2.206Task.putmaxnumcone() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322 A.2.207Task.putmaxnumqnz() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323
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 39 m
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5.4. SEMIDEFINITE OPTIMIZATION 41 4
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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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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
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
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531 rescode.err numconlim Maximum n
Page 555 and 556:
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
Page 561 and 562:
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
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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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
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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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