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

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594 APPENDIX F. MOSEK FILE FORMATS QSECTION obj x1 x1 2.0 x1 x3 -1.0 x2 x2 0.2 x3 x3 2.0 ENDATA Regarding the QSECTIONs please note that: • Only one QSECTION is allowed for each constraint. • The QSECTIONs can appear in an arbitrary order after the COLUMNS section. • All variable names occurring in the QSECTION must already be specified in the COLUMNS section. • All entries specified in a QSECTION are assumed to belong to the lower triangular part of the quadratic term of Q . F.1.1.10 BOUNDS (optional) In the BOUNDS section changes to the default bounds vectors l x and u x are specified. The default bounds vectors are l x = 0 and u x = ∞ . Moreover, it is possible to specify several sets of bound vectors. A record in this section has the form ?? [name] [vname1] [value1] where the requirements for each field are: Field Starting Maximum Re- Description position width quired ?? 2 2 Yes Bound key [name] 5 8 Yes Name of the BOUNDS vector [vname1] 15 8 Yes Variable name [value1] 25 12 No Numerical value Hence, a record in the BOUNDS section has the following interpretation: [name] is the name of the bound vector and [vname1] is the name of the variable which bounds are modified by the record. ?? and [value1] are used to modify the bound vectors according to the following table: ?? lj x u x j Made integer (added to J ) FR −∞ ∞ No FX v 1 v 1 No LO v 1 unchanged No MI −∞ unchanged No PL unchanged ∞ No UP unchanged v 1 No BV 0 1 Yes LI ⌈v 1 ⌉ unchanged Yes UI unchanged ⌊v 1 ⌋ Yes
F.1. THE MPS FILE FORMAT 595 v 1 is the value specified by [value1]. F.1.1.11 CSECTION (optional) The purpose of the CSECTION is to specify the constraint in (F.1). x ∈ C. It is assumed that C satisfies the following requirements. Let x t ∈ R nt , t = 1, . . . , k be vectors comprised of parts of the decision variables x so that each decision variable is a member of exactly one vector x t , for example Next define ⎡ x 1 = ⎣ x 1 x 4 x 7 where C t must have one of the following forms • R set: ⎤ ⎦ and x 2 = ⎡ ⎢ ⎣ x 6 x 5 x 3 x 2 ⎤ ⎥ ⎦ . C := { x ∈ R n : x t ∈ C t , t = 1, . . . , k } • Quadratic cone: C t = {x ∈ R nt }. ⎧ ⎨ C t = ⎩ x ∈ ∑ Rnt : x 1 ≥ √ nt j=2 x 2 j ⎫ ⎬ ⎭ . (F.2) • Rotated quadratic cone: ⎧ ⎨ C t = ⎩ x ∈ Rnt : 2x 1 x 2 ≥ ⎫ ∑n t ⎬ x 2 j, x 1 , x 2 ≥ 0 ⎭ . j=3 (F.3)
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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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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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Page 607 and 608: Appendix E Troubleshooting When cre
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Page 611 and 612: F.1. THE MPS FILE FORMAT 589 Fields
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Page 635 and 636: F.3. THE OPF FORMAT 613 [bounds] [b
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Page 641 and 642: Appendix G Problem analyzer example
Page 643 and 644: G.2. ARKI001 621 2 476 45.42 48.19
Page 645 and 646: G.4. PROBLEM WITH BOTH LINEAR AND C
Page 647 and 648: Bibliography [1] Chvátal, V.. Line
Page 649 and 650: Index analyzenames (Task method), 2
Page 651 and 652: INDEX 629 getpcni (Task method), 25
Page 653 and 654: INDEX 631 putbarablocktriplet (Task
Page 655 and 656: INDEX 633 rescode.err inv numj, 521
Page 657 and 658: INDEX 635 rescode.err sen bound inv
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