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

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114 CHAPTER 8. A CASE STUDY The following example code demonstrates how to implement the model (8.14). 1 """ 2 File : case portfolio 3.py 3 [ case portfolio 3.py ] 4 Copyright : Copyright (c) MOSEK ApS, Denmark. All rights reserved. 5 6 Description : Implements a basic portfolio optimization model. 7 """ 8 10 9 import mosek 11 try: 12 from numpy import zeros 13 except ImportError: 14 from mosek.array import zeros 15 16 def streamprinter(text): 17 print("%s" % text), 18 19 if name == ’ main ’: 20 21 n = 3 22 gamma = 0.05 23 mu = [0.1073, 0.0737, 0.0627] 24 GT = [[0.1667, 0.0232, 0.0013], 25 [0.0000, 0.1033, -0.0022], 26 [0.0000, 0.0000, 0.0338]] 27 x0 = [0.0, 0.0, 0.0] 28 w = 1.0 29 m = [0.01, 0.01, 0.01] 30 31 # This value has no significance. 32 inf = 0.0 33 34 with mosek.Env() as env: 35 with env.Task(0,0) as task: 36 task.set Stream(mosek.streamtype.log,streamprinter) 37 38 rtemp = w 39 for j in range(0,n): 40 rtemp += x0[j] 41 42 # Constraints. 43 task.appendcons(1+9*n) 44 task.putconbound(0,mosek.boundkey.fx,rtemp,rtemp) 45 task.putconname(0,"budget") 46 47 task.putconboundlist(range(1+0,1+n),n*[mosek.boundkey.fx],n*[0.0],n*[0.0]) 48 for j in range(1,1+n) : 49 task.putconname(j,"GT[%d]" % j) 50 51 task.putconboundlist(range(1+n,1+2*n),n*[mosek.boundkey.lo],[-x0[j] for j in range(0,n)],n*[inf]) 52 for i in range(0,n): 53 task.putconname(1+n+i,"zabs1[%d]" % (1+i)) 54 55 task.putconboundlist(range(1+2*n,1+3*n),n*[mosek.boundkey.lo],x0,n*[inf])
8.1. PORTFOLIO OPTIMIZATION 115 56 for i in range(0,n): 57 task.putconname(1+2*n+i,"zabs2[%d]" % (1+i)) 58 59 task.putconboundlist(range(1+3*n,1+3*n+3*n),3*n*[mosek.boundkey.fx],3*n*[0.],3*n*[0.0]) 60 for i in range(0,n): 61 for k in range(0,n): 62 task.putconname(1+3*n+3*i+k,"f[%d,%d]" % (1+i,1+k)) 63 64 task.putconboundlist(range(1+6*n,1+9*n),3*n*[mosek.boundkey.fx], 65 3*[0.0, -1.0/8.0, 0.0],3*[0.0, -1.0/8.0, 0.0]) 66 for i in range(0,n) : 67 for k in range(0,n): 68 task.putconname(1+6*n+3*i+k,"g[%d,%d]" % (1+i,1+k)) 69 70 # Offset of variables into the API variable. 71 offsetx = 0 72 offsets = n 73 offsett = n+1 74 offsetc = 2*n+1 75 offsetv = 3*n+1 76 offsetz = 4*n+1 77 offsetf = 5*n+1 78 offsetg = 8*n+1 79 80 # Variables. 81 task.appendvars(1+11*n) 82 83 # x variables. 84 task.putclist(range(offsetx+0,offsetx+n),mu) 85 task.putaijlist(n*[0],range(offsetx+0,offsetx+n),n*[1.0]) 86 for j in range(0,n): 87 task.putaijlist(n*[1+j],range(offsetx+0,offsetx+n),GT[j]) 88 task.putaij(1+n+j,offsetx+j,-1.0) 89 task.putaij(1+2*n+j,offsetx+j,1.0) 90 91 task.putvarboundlist(range(offsetx+0,offsetx+n),n*[mosek.boundkey.lo],n*[0.0],n*[inf]) 92 for j in range(0,n): 93 task.putvarname(offsetx+j,"x[%d]" % (1+j)) 94 95 # s variable. 96 task.putvarbound(offsets+0,mosek.boundkey.fx,gamma,gamma) 97 task.putvarname(offsets+0,"s") 98 99 # t variables. 100 task.putaijlist(range(1,n+1),range(offsett+0,offsett+n),n*[-1.0]) 101 task.putvarboundlist(range(offsett+0,offsett+n),n*[mosek.boundkey.fr],n*[-inf],n*[inf]) 102 for j in range(0,n): 103 task.putvarname(offsett+j,"t[%d]" % (1+j)) 104 105 # c variables. 106 task.putaijlist(n*[0],range(offsetc,offsetc+n),m) 107 task.putaijlist(range(1+3*n+1,1+6*n+1,3),range(offsetc,offsetc+n),n*[1.0]) 108 task.putvarboundlist(range(offsetc,offsetc+n),n*[mosek.boundkey.fr],n*[-inf],n*[inf]) 109 for j in range(0,n): 110 task.putvarname(offsetc+j,"c[%d]" % (1+j)) 111 112 # v variables. 113 task.putaijlist(range(1+3*n+0,1+6*n+0,3),range(offsetv,offsetv+n),n*[1.0])
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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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Page 119 and 120: Chapter 8 A case study 8.1 Portfoli
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Page 147 and 148: 10.1. LINEAR OPTIMIZATION 125 be a
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Page 177 and 178: Chapter 12 The optimizers for mixed
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Page 185 and 186: 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 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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