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

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36 CHAPTER 5. BASIC API TUTORIAL 1 # 5.3.1.1 Source code [ cqo1.py ] 2 # Copyright: Copyright (c) MOSEK ApS, Denmark. All rights reserved. 3 # 4 # File: cqo1.py 5 # 6 # Purpose: Demonstrates how to solve small linear 7 # optimization problem using the MOSEK Python API. 8 ## 9 10 import sys 11 12 import mosek 13 # If numpy is installed, use that, otherwise use the 14 # Mosek’s array module. 15 try: 16 from numpy import array,zeros,ones 17 except ImportError: 18 from mosek.array import array, zeros, ones 19 20 # Since the actual value of Infinity is ignores, we define it solely 21 # for symbolic purposes: 22 inf = 0.0 23 24 # Define a stream printer to grab output from MOSEK 25 def streamprinter(text): 26 sys.stdout.write(text) 27 sys.stdout.flush() 28 29 # We might write everything directly as a script, but it looks nicer 30 # to create a function. 31 def main (): 32 # Make a MOSEK environment 33 env = mosek.Env () 34 # Attach a printer to the environment 35 env.set Stream (mosek.streamtype.log, streamprinter) 36 37 # Create a task 38 task = env.Task(0,0) 39 # Attach a printer to the task 40 task.set Stream (mosek.streamtype.log, streamprinter) 41 42 bkc = [ mosek.boundkey.fx ] 43 blc = [ 1.0 ] 44 buc = [ 1.0 ] 45 46 c = [ 0.0, 0.0, 0.0, 47 1.0, 1.0, 1.0 ] 48 bkx = [ mosek.boundkey.lo,mosek.boundkey.lo,mosek.boundkey.lo, 49 mosek.boundkey.fr,mosek.boundkey.fr,mosek.boundkey.fr ] 50 blx = [ 0.0, 0.0, 0.0, 51 -inf, -inf, -inf ] 52 bux = [ inf, inf, inf, 53 inf, inf, inf ] 54 55 asub = [ array([0]), array([0]), array([0]) ]
5.3. CONIC QUADRATIC OPTIMIZATION 37 56 aval = [ array([1.0]), array([1.0]), array([2.0]) ] 57 58 59 numvar = len(bkx) 60 numcon = len(bkc) 61 NUMANZ = 4 62 # Append ’numcon’ empty constraints. 63 # The constraints will initially have no bounds. 64 task.appendcons(numcon) 65 66 #Append ’numvar’ variables. 67 # The variables will initially be fixed at zero (x=0). 68 task.appendvars(numvar) 69 70 for j in range(numvar): 71 # Set the linear term c j in the objective. 72 task.putcj(j,c[j]) 73 # Set the bounds on variable j 74 # blx[j]
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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
Page 7 and 8: CONTENTS vii 14.2.1 Caveats . . . .
Page 9 and 10: CONTENTS ix A.2.70 Task.getdviolvar
Page 11 and 12: CONTENTS xi A.2.162Task.isdouparnam
Page 13 and 14: CONTENTS xiii A.2.254Task.readparam
Page 15 and 16: CONTENTS xv B.1.45 dparam.mio near
Page 17 and 18: CONTENTS xvii B.2.68 iparam.log sim
Page 19 and 20: CONTENTS xix B.2.160iparam.sim refa
Page 21 and 22: CONTENTS xxi D.18 Long integer info
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
Page 49 and 50: 5.2. LINEAR OPTIMIZATION 27 Load a
Page 51 and 52: 5.2. LINEAR OPTIMIZATION 29 Optimiz
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Page 61 and 62: 5.4. SEMIDEFINITE OPTIMIZATION 39 m
Page 63 and 64: 5.4. SEMIDEFINITE OPTIMIZATION 41 4
Page 65 and 66: 5.4. SEMIDEFINITE OPTIMIZATION 43 1
Page 67 and 68: 5.5. QUADRATIC OPTIMIZATION 45 with
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Page 71 and 72: 5.5. QUADRATIC OPTIMIZATION 49 5.5.
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Page 75 and 76: 5.6. THE SOLUTION SUMMARY 53 • Th
Page 77 and 78: 5.7. INTEGER OPTIMIZATION 55 21 # f
Page 79 and 80: 5.7. INTEGER OPTIMIZATION 57 137 sy
Page 81 and 82: 5.8. THE SOLUTION SUMMARY FOR MIXED
Page 83 and 84: 5.9. RESPONSE HANDLING 61 Note that
Page 85 and 86: 5.10. PROBLEM MODIFICATION AND REOP
Page 87 and 88: 5.10. PROBLEM MODIFICATION AND REOP
Page 89 and 90: 5.11. SOLUTION ANALYSIS 67 151 # Pu
Page 91 and 92: 5.13. CONVENTIONS EMPLOYED IN THE A
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Page 101 and 102: 6.1. SEPARABLE CONVEX (SCOPT) INTER
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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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