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

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viii CONTENTS A.2.24 Task.getarow() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 A.2.25 Task.getarownumnz() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218 A.2.26 Task.getarowslicetrip() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218 A.2.27 Task.getaslice() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 A.2.28 Task.getaslicenumnz() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 A.2.29 Task.getbarablocktriplet() . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220 A.2.30 Task.getbaraidx() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 A.2.31 Task.getbaraidxij() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 A.2.32 Task.getbaraidxinfo() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 A.2.33 Task.getbarasparsity() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 A.2.34 Task.getbarcblocktriplet() . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 A.2.35 Task.getbarcidx() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224 A.2.36 Task.getbarcidxinfo() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224 A.2.37 Task.getbarcidxj() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 A.2.38 Task.getbarcsparsity() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 A.2.39 Task.getbarsj() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226 A.2.40 Task.getbarvarname() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226 A.2.41 Task.getbarvarnameindex() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 A.2.42 Task.getbarvarnamelen() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 A.2.43 Task.getbarxj() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228 A.2.44 Task.getbound() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228 A.2.45 Task.getboundslice() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 A.2.46 Task.getc() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 A.2.47 Task.getcfix() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230 A.2.48 Task.getcj() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230 A.2.49 Task.getconbound() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231 A.2.50 Task.getconboundslice() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231 A.2.51 Task.getcone() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232 A.2.52 Task.getconeinfo() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232 A.2.53 Task.getconename() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233 A.2.54 Task.getconenameindex() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233 A.2.55 Task.getconenamelen() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234 A.2.56 Task.getconname() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234 A.2.57 Task.getconnameindex() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 A.2.58 Task.getconnamelen() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 A.2.59 Task.getcslice() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236 A.2.60 Task.getdbi() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236 A.2.61 Task.getdcni() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 A.2.62 Task.getdeqi() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 A.2.63 Task.getdimbarvarj() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238 A.2.64 Task.getdouinf() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239 A.2.65 Task.getdouparam() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239 A.2.66 Task.getdualobj() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239 A.2.67 Task.getdviolbarvar() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240 A.2.68 Task.getdviolcon() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240 A.2.69 Task.getdviolcones() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241
CONTENTS ix A.2.70 Task.getdviolvar() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242 A.2.71 Task.getinfeasiblesubproblem() . . . . . . . . . . . . . . . . . . . . . . . . . 243 A.2.72 Task.getinti() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243 A.2.73 Task.getintinf() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244 A.2.74 Task.getintparam() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244 A.2.75 Task.getlenbarvarj() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245 A.2.76 Task.getlintinf() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245 A.2.77 Task.getmaxnumanz() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245 A.2.78 Task.getmaxnumbarvar() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246 A.2.79 Task.getmaxnumcon() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246 A.2.80 Task.getmaxnumcone() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247 A.2.81 Task.getmaxnumqnz() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247 A.2.82 Task.getmaxnumvar() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247 A.2.83 Task.getmemusage() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248 A.2.84 Task.getnumanz() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248 A.2.85 Task.getnumanz64() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248 A.2.86 Task.getnumbarablocktriplets() . . . . . . . . . . . . . . . . . . . . . . . . . 249 A.2.87 Task.getnumbaranz() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249 A.2.88 Task.getnumbarcblocktriplets() . . . . . . . . . . . . . . . . . . . . . . . . . 249 A.2.89 Task.getnumbarcnz() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250 A.2.90 Task.getnumbarvar() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250 A.2.91 Task.getnumcon() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250 A.2.92 Task.getnumcone() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 A.2.93 Task.getnumconemem() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 A.2.94 Task.getnumintvar() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 A.2.95 Task.getnumparam() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252 A.2.96 Task.getnumqconknz() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252 A.2.97 Task.getnumqconknz64() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252 A.2.98 Task.getnumqobjnz() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253 A.2.99 Task.getnumsymmat() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253 A.2.100Task.getnumvar() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254 A.2.101Task.getobjname() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254 A.2.102Task.getobjnamelen() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254 A.2.103Task.getobjsense() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255 A.2.104Task.getpbi() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255 A.2.105Task.getpcni() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256 A.2.106Task.getpeqi() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256 A.2.107Task.getprimalobj() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257 A.2.108Task.getprobtype() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257 A.2.109Task.getprosta() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258 A.2.110Task.getpviolbarvar() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258 A.2.111Task.getpviolcon() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259 A.2.112Task.getpviolcones() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259 A.2.113Task.getpviolvar() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260 A.2.114Task.getqconk() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261 A.2.115Task.getqobj() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261
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Page 3 and 4: Contents 1 Changes and new features
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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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5.3. CONIC QUADRATIC OPTIMIZATION 3
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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
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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
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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
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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
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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
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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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