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

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190 CHAPTER 15. SENSITIVITY ANALYSIS Supply Demand 400 Plant 1 1 2 Store 1 800 Store 2 100 1 1200 Plant 2 5 Store 3 500 1000 Plant 3 2 1 2 Store 4 500 Figure 15.2: Supply, demand and cost of transportation.
15.4. SENSITIVITY ANALYSIS FOR LINEAR PROBLEMS 191 Basis type Con. β 1 β 2 σ 1 σ 2 1 −300.00 0.00 3.00 3.00 2 −700.00 +∞ 0.00 0.00 3 −500.00 0.00 3.00 3.00 4 −0.00 500.00 4.00 4.00 5 −0.00 300.00 5.00 5.00 6 −0.00 700.00 5.00 5.00 7 −500.00 700.00 2.00 2.00 Var. β 1 β 2 σ 1 σ 2 x 11 −∞ 300.00 0.00 0.00 x 12 −∞ 100.00 0.00 0.00 x 23 −∞ 0.00 0.00 0.00 x 24 −∞ 500.00 0.00 0.00 x 31 −∞ 500.00 0.00 0.00 x 33 −∞ 500.00 0.00 0.00 x 34 −0.000000 500.00 2.00 2.00 Optimal partition type Con. β 1 β 2 σ 1 σ 2 1 −300.00 500.00 3.00 1.00 2 −700.00 +∞ −0.00 −0.00 3 −500.00 500.00 3.00 1.00 4 −500.00 500.00 2.00 4.00 5 −100.00 300.00 3.00 5.00 6 −500.00 700.00 3.00 5.00 7 −500.00 700.00 2.00 2.00 Var. β 1 β 2 σ 1 σ 2 x 11 −∞ 300.00 0.00 0.00 x 12 −∞ 100.00 0.00 0.00 x 23 −∞ 500.00 0.00 2.00 x 24 −∞ 500.00 0.00 0.00 x 31 −∞ 500.00 0.00 0.00 x 33 −∞ 500.00 0.00 0.00 x 34 −∞ 500.00 0.00 2.00 Table 15.1: Ranges and shadow prices related to bounds on constraints and variables. Left: Results for the basis type sensitivity analysis. Right: Results for the optimal partition type sensitivity analysis. x 11 + x 12 ≤ 400, x 23 + x 24 ≤ 1200, x 31 + x 33 + x 34 ≤ 1000, x 11 + x 31 = 800, x 12 = 100, x 23 + x 33 = 500, x 24 + x 34 = 500, x 11 , x 12 , x 23 , x 24 , x 31 , x 33 , x 34 ≥ 0. (15.3) The basis type and the optimal partition type sensitivity results for the transportation problem are shown in Table 15.1 and 15.2 respectively. Examining the results from the optimal partition type sensitivity analysis we see that for constraint number 1 we have σ 1 ≠ σ 2 and β 1 ≠ β 2 . Therefore, we have a left linearity interval of [−300, 0] and a right interval of [0, 500]. The corresponding left and right shadow prices are 3 and 1 respectively. This implies that if the upper bound on constraint 1 increases by β ∈ [0, β 1 ] = [0, 500] then the optimal objective value will decrease by the value σ 2 β = 1β. Correspondingly, if the upper bound on constraint 1 is decreased by
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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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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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Page 163 and 164: 11.2. LINEAR OPTIMIZATION 141 Whene
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Page 167 and 168: 11.2. LINEAR OPTIMIZATION 145 • R
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Page 185 and 186: Chapter 13 The analyzers 13.1 The p
Page 187 and 188: 13.1. THE PROBLEM ANALYZER 165 Cons
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Page 199 and 200: Chapter 14 Primal feasibility repai
Page 201 and 202: 14.2. AUTOMATIC REPAIR 179 One way
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Page 221 and 222: Appendix A API reference This chapt
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Page 225 and 226: A.1. EXCEPTIONS 203 • Task.putvar
Page 227 and 228: A.2. CLASS TASK 205 Arguments which
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A.2. CLASS TASK 241 Computes the vi
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A.2. CLASS TASK 243 A.2.71 Task.get
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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 281 Description: Ob
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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 291 Description: Ob
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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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