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

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118 CHAPTER 8. A CASE STUDY [con ’f[1,2]’] [con ’f[1,3]’] [con ’f[2,1]’] [con ’f[2,2]’] [con ’f[2,3]’] [con ’f[3,1]’] [con ’f[3,2]’] [con ’f[3,3]’] [con ’g[1,1]’] [con ’g[1,2]’] [con ’g[1,3]’] [con ’g[2,1]’] [con ’g[2,2]’] [con ’g[2,3]’] [con ’g[3,1]’] [con ’g[3,2]’] [con ’g[3,3]’] [/constraints] ’c[1]’ - ’f[1,2]’ = 0e+000 [/con] ’z[1]’ - ’f[1,3]’ = 0e+000 [/con] ’v[2]’ - ’f[2,1]’ = 0e+000 [/con] ’c[2]’ - ’f[2,2]’ = 0e+000 [/con] ’z[2]’ - ’f[2,3]’ = 0e+000 [/con] ’v[3]’ - ’f[3,1]’ = 0e+000 [/con] ’c[3]’ - ’f[3,2]’ = 0e+000 [/con] ’z[3]’ - ’f[3,3]’ = 0e+000 [/con] ’z[1]’ - ’g[1,1]’ = 0e+000 [/con] - ’g[1,2]’ = -1.25e-001 [/con] ’v[1]’ - ’g[1,3]’ = 0e+000 [/con] ’z[2]’ - ’g[2,1]’ = 0e+000 [/con] - ’g[2,2]’ = -1.25e-001 [/con] ’v[2]’ - ’g[2,3]’ = 0e+000 [/con] ’z[3]’ - ’g[3,1]’ = 0e+000 [/con] - ’g[3,2]’ = -1.25e-001 [/con] ’v[3]’ - ’g[3,3]’ = 0e+000 [/con] [bounds] [b] 0
Chapter 9 Usage guidelines The purpose of this chapter is to present some general guidelines to follow when using MOSEK. 9.1 Verifying the results The main purpose of MOSEK is to solve optimization problems and therefore the most fundamental question to be asked is whether the solution reported by MOSEK is a solution to the desired optimization problem. There can be several reasons why it might be not case. The most prominent reasons are: • A wrong problem. The problem inputted to MOSEK is simply not the right problem, i.e. some of the data may have been corrupted or the model has been incorrectly built. • Numerical issues. The problem is badly scaled or otherwise badly posed. • Other reasons. E.g. not enough memory or an explicit user request to stop. The first step in verifying that MOSEK reports the expected solution is to inspect the solution summary generated by MOSEK. The solution summary provides information about • the problem and solution statuses, • objective value and infeasibility measures for the primal solution, and • objective value and infeasibility measures for the dual solution, where applicable. By inspecting the solution summary it can be verified that MOSEK produces a feasible solution, and, in the continuous case, the optimality can be checked using the dual solution. Furthermore, the problem itself ca be inspected using the problem analyzer discussed in section 13.1. If the summary reports conflicting information (e.g. a solution status that does not match the actual solution), or the cause for terminating the solver before a solution was found cannot be traced back to 119
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The MOSEK Python optimizer API manu
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Contents 1 Changes and new features
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CONTENTS v 8 A case study 97 8.1 Po
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CONTENTS vii 14.2.1 Caveats . . . .
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CONTENTS ix A.2.70 Task.getdviolvar
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CONTENTS xi A.2.162Task.isdouparnam
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CONTENTS xiii A.2.254Task.readparam
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CONTENTS xv B.1.45 dparam.mio near
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CONTENTS xvii B.2.68 iparam.log sim
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CONTENTS xix B.2.160iparam.sim refa
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CONTENTS xxi D.18 Long integer info
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Contact information Phone +45 3917
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License agreement Before using the
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Chapter 1 Changes and new features
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1.4. API CHANGES 7 1.3.3 Mixed-inte
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1.10. SUMMARY OF API CHANGES 9 •
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Chapter 2 About this manual This ma
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Chapter 3 Getting support and help
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Chapter 4 Testing installation and
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Chapter 5 Basic API tutorial In thi
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5.1. THE BASICS 23 5 # 6 # Purpose:
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5.2. LINEAR OPTIMIZATION 25 and the
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5.2. LINEAR OPTIMIZATION 27 Load a
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5.2. LINEAR OPTIMIZATION 29 Optimiz
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5.2. LINEAR OPTIMIZATION 31 88 task
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5.2. LINEAR OPTIMIZATION 33 51 mose
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5.3. CONIC QUADRATIC OPTIMIZATION 3
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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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Page 99 and 100: Chapter 6 Nonlinear API tutorial Th
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Page 107 and 108: Chapter 7 Advanced API tutorial Thi
Page 109 and 110: 7.1. THE PROGRESS CALL-BACK 87 71 p
Page 111 and 112: 7.2. SOLVING LINEAR SYSTEMS INVOLVI
Page 119 and 120: Chapter 8 A case study 8.1 Portfoli
Page 121 and 122: 8.1. PORTFOLIO OPTIMIZATION 99 e T
Page 123 and 124: 8.1. PORTFOLIO OPTIMIZATION 101 is
Page 125 and 126: 8.1. PORTFOLIO OPTIMIZATION 103 15
Page 129 and 130: 8.1. PORTFOLIO OPTIMIZATION 107 8.1
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Page 135 and 136: 8.1. PORTFOLIO OPTIMIZATION 113 Var
Page 139: 8.1. PORTFOLIO OPTIMIZATION 117 172
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Page 145 and 146: Chapter 10 Problem formulation and
Page 147 and 148: 10.1. LINEAR OPTIMIZATION 125 be a
Page 149 and 150: 10.2. CONIC QUADRATIC OPTIMIZATION
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Page 153 and 154: 10.3. SEMIDEFINITE OPTIMIZATION 131
Page 155 and 156: 10.4. QUADRATIC AND QUADRATICALLY C
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Page 159 and 160: 11.1. HOW AN OPTIMIZER WORKS 137 11
Page 161 and 162: 11.2. LINEAR OPTIMIZATION 139 11.2.
Page 163 and 164: 11.2. LINEAR OPTIMIZATION 141 Whene
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Page 167 and 168: 11.2. LINEAR OPTIMIZATION 145 • R
Page 169 and 170: 11.5. NONLINEAR CONVEX OPTIMIZATION
Page 171 and 172: 11.6. SOLVING PROBLEMS IN PARALLEL
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Page 181 and 182: 12.5. TERMINATION CRITERION 159 •
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Page 187 and 188: 13.1. THE PROBLEM ANALYZER 165 Cons
Page 189 and 190: 13.2. ANALYZING INFEASIBLE PROBLEMS
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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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