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

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116 CHAPTER 8. A CASE STUDY 114 task.putaijlist(range(1+6*n+2,1+9*n+2,3),range(offsetv,offsetv+n),n*[1.0]) 115 task.putvarboundlist(range(offsetv,offsetv+n),n*[mosek.boundkey.fr],n*[-inf],n*[inf]) 116 for j in range(0,n): 117 task.putvarname(offsetv+j,"v[%d]" % (1+j)) 118 119 # z variables. 120 task.putaijlist(range(1+1*n,1+2*n),range(offsetz,offsetz+n),n*[1.0]) 121 task.putaijlist(range(1+2*n,1+3*n),range(offsetz,offsetz+n),n*[1.0]) 122 task.putaijlist(range(1+3*n+2,1+6*n+2,3),range(offsetz,offsetz+n),n*[1.0]) 123 task.putaijlist(range(1+6*n+0,1+9*n+0,3),range(offsetz,offsetz+n),n*[1.0]) 124 task.putvarboundlist(range(offsetz,offsetz+n),n*[mosek.boundkey.fr],n*[-inf],n*[inf]) 125 for j in range(0,n): 126 task.putvarname(offsetz+j,"z[%d]" % (1+j)) 127 128 # f variables. 129 for j in range(0,n): 130 for k in range(0,n): 131 task.putaij(1+3*n+3*j+k,offsetf+3*j+k,-1.0) 132 task.putvarbound(offsetf+3*j+k,mosek.boundkey.fr,-inf,inf) 133 task.putvarname(offsetf+3*j+k,"f[%d,%d]" % (1+j,1+k)) 134 135 # g variables. 136 for j in range(0,n): 137 for k in range(0,n): 138 task.putaij(1+6*n+3*j+k,offsetg+3*j+k,-1.0) 139 task.putvarbound(offsetg+3*j+k,mosek.boundkey.fr,-inf,inf) 140 task.putvarname(offsetg+3*j+k,"g[%d,%d]" % (1+j,1+k)) 141 142 task.appendcone(mosek.conetype.quad,0.0,[offsets] + range(offsett,offsett+n)) 143 task.putconename(0,"stddev") 144 145 for k in range(0,n): 146 task.appendconeseq(mosek.conetype.rquad,0.0,3,offsetf+3*k) 147 task.putconename(1+k,"f[%d]" % (1+k)) 148 149 for k in range(0,n): 150 task.appendconeseq(mosek.conetype.rquad,0.0,3,offsetg+3*k) 151 task.putconename(1+n+k,"g[%d]" % (1+k)) 152 153 task.putobjsense(mosek.objsense.maximize) 154 155 # Turn all log output off. 156 # task.putintparam(mosek.iparam.log,0) 157 158 # Dump the problem to a human readable OPF file. 159 #task.writedata("dump.opf") 160 161 task.optimize() 162 163 # Display the solution summary for quick inspection of results. 164 task.solutionsummary(mosek.streamtype.msg) 165 166 expret = 0.0 167 x = zeros(n,float) 168 task.getxxslice(mosek.soltype.itr,offsetx+0,offsetx+n,x) 169 for j in range(0,n): 170 expret += mu[j]*x[j] 171
8.1. PORTFOLIO OPTIMIZATION 117 172 stddev = zeros(1,float) 173 task.getxxslice(mosek.soltype.itr,offsets+0,offsets+1,stddev) 174 175 print("\nExpected return %e for gamma %e\n" % (expret,stddev[0])) The example code above produces the result Interior-point solution summary Problem status : PRIMAL AND DUAL FEASIBLE Solution status : OPTIMAL Primal. obj: 7.4390660228e-002 Viol. con: 2e-007 var: 0e+000 cones: 1e-009 Dual. obj: 7.4390669047e-002 Viol. con: 1e-008 var: 1e-008 cones: 0e+000 Expected return 7.439066e-02 for gamma 5.000000e-02 If the problem is dumped to an OPF formatted file, then it has the following content. [comment] Written by MOSEK version 7.0.0.86 Date 01-10-13 Time 07:47:34 [/comment] [hints] [hint NUMVAR] 34 [/hint] [hint NUMCON] 28 [/hint] [hint NUMANZ] 60 [/hint] [hint NUMQNZ] 0 [/hint] [hint NUMCONE] 7 [/hint] [/hints] [variables disallow new variables] ’x[1]’ ’x[2]’ ’x[3]’ s ’t[1]’ ’t[2]’ ’t[3]’ ’c[1]’ ’c[2]’ ’c[3]’ ’v[1]’ ’v[2]’ ’v[3]’ ’z[1]’ ’z[2]’ ’z[3]’ ’f[1,1]’ ’f[1,2]’ ’f[1,3]’ ’f[2,1]’ ’f[2,2]’ ’f[2,3]’ ’f[3,1]’ ’f[3,2]’ ’f[3,3]’ ’g[1,1]’ ’g[1,2]’ ’g[1,3]’ ’g[2,1]’ ’g[2,2]’ ’g[2,3]’ ’g[3,1]’ ’g[3,2]’ ’g[3,3]’ [/variables] [objective maximize] 1.073e-001 ’x[1]’ + 7.37e-002 ’x[2]’ + 6.270000000000001e-002 ’x[3]’ [/objective] [constraints] [con ’budget’] ’x[1]’ + ’x[2]’ + ’x[3]’ + 1e-002 ’c[1]’ + 1e-002 ’c[2]’ + 1e-002 ’c[3]’ = 1e+000 [/con] [con ’GT[1]’] 1.667e-001 ’x[1]’ + 2.32e-002 ’x[2]’ + 1.3e-003 ’x[3]’ - ’t[1]’ = 0e+000 [/con] [con ’GT[2]’] 1.033e-001 ’x[2]’ - 2.2e-003 ’x[3]’ - ’t[2]’ = 0e+000 [/con] [con ’GT[3]’] 3.38e-002 ’x[3]’ - ’t[3]’ = 0e+000 [/con] [con ’zabs1[1]’] 0e+000
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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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Page 141 and 142: Chapter 9 Usage guidelines The purp
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Page 147 and 148: 10.1. LINEAR OPTIMIZATION 125 be a
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Page 159 and 160: 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 177 and 178: Chapter 12 The optimizers for mixed
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Page 181 and 182: 12.5. TERMINATION CRITERION 159 •
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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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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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