The MOSEK optimization toolbox for MATLAB manual Version 7.0 (Revision 141)

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xiv CONTENTS 23.2.128MSK IPAR READ DATA FORMAT . . . . . . . . . . . . . . . . . . . . . . . . . 329 23.2.129MSK IPAR READ KEEP FREE CON . . . . . . . . . . . . . . . . . . . . . . . 330 23.2.130MSK IPAR READ LP DROP NEW VARS IN BOU . . . . . . . . . . . . . . . . 330 23.2.131MSK IPAR READ LP QUOTED NAMES . . . . . . . . . . . . . . . . . . . . . 331 23.2.132MSK IPAR READ MPS FORMAT . . . . . . . . . . . . . . . . . . . . . . . . . 331 23.2.133MSK IPAR READ MPS KEEP INT . . . . . . . . . . . . . . . . . . . . . . . . . 331 23.2.134MSK IPAR READ MPS OBJ SENSE . . . . . . . . . . . . . . . . . . . . . . . . 332 23.2.135MSK IPAR READ MPS RELAX . . . . . . . . . . . . . . . . . . . . . . . . . . . 332 23.2.136MSK IPAR READ MPS WIDTH . . . . . . . . . . . . . . . . . . . . . . . . . . 333 23.2.137MSK IPAR READ QNZ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333 23.2.138MSK IPAR READ TASK IGNORE PARAM . . . . . . . . . . . . . . . . . . . . 333 23.2.139MSK IPAR READ VAR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334 23.2.140MSK IPAR SENSITIVITY ALL . . . . . . . . . . . . . . . . . . . . . . . . . . . 334 23.2.<strong>141</strong>MSK IPAR SENSITIVITY OPTIMIZER . . . . . . . . . . . . . . . . . . . . . . 334 23.2.142MSK IPAR SENSITIVITY TYPE . . . . . . . . . . . . . . . . . . . . . . . . . . 335 23.2.143MSK IPAR SIM BASIS FACTOR USE . . . . . . . . . . . . . . . . . . . . . . . 335 23.2.144MSK IPAR SIM DEGEN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336 23.2.145MSK IPAR SIM DUAL CRASH . . . . . . . . . . . . . . . . . . . . . . . . . . . 336 23.2.146MSK IPAR SIM DUAL PHASEONE METHOD . . . . . . . . . . . . . . . . . . 337 23.2.147MSK IPAR SIM DUAL RESTRICT SELECTION . . . . . . . . . . . . . . . . . 337 23.2.148MSK IPAR SIM DUAL SELECTION . . . . . . . . . . . . . . . . . . . . . . . . 337 23.2.149MSK IPAR SIM EXPLOIT DUPVEC . . . . . . . . . . . . . . . . . . . . . . . . 338 23.2.150MSK IPAR SIM HOTSTART . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338 23.2.151MSK IPAR SIM HOTSTART LU . . . . . . . . . . . . . . . . . . . . . . . . . . 339 23.2.152MSK IPAR SIM INTEGER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339 23.2.153MSK IPAR SIM MAX ITERATIONS . . . . . . . . . . . . . . . . . . . . . . . . 339 23.2.154MSK IPAR SIM MAX NUM SETBACKS . . . . . . . . . . . . . . . . . . . . . . 340 23.2.155MSK IPAR SIM NON SINGULAR . . . . . . . . . . . . . . . . . . . . . . . . . 340 23.2.156MSK IPAR SIM PRIMAL CRASH . . . . . . . . . . . . . . . . . . . . . . . . . . 340 23.2.157MSK IPAR SIM PRIMAL PHASEONE METHOD . . . . . . . . . . . . . . . . 341 23.2.158MSK IPAR SIM PRIMAL RESTRICT SELECTION . . . . . . . . . . . . . . . 341 23.2.159MSK IPAR SIM PRIMAL SELECTION . . . . . . . . . . . . . . . . . . . . . . 341 23.2.160MSK IPAR SIM REFACTOR FREQ . . . . . . . . . . . . . . . . . . . . . . . . 342 23.2.161MSK IPAR SIM REFORMULATION . . . . . . . . . . . . . . . . . . . . . . . . 342 23.2.162MSK IPAR SIM SAVE LU . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343 23.2.163MSK IPAR SIM SCALING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343 23.2.164MSK IPAR SIM SCALING METHOD . . . . . . . . . . . . . . . . . . . . . . . 344 23.2.165MSK IPAR SIM SOLVE FORM . . . . . . . . . . . . . . . . . . . . . . . . . . . 344 23.2.166MSK IPAR SIM STABILITY PRIORITY . . . . . . . . . . . . . . . . . . . . . . 344 23.2.167MSK IPAR SIM SWITCH OPTIMIZER . . . . . . . . . . . . . . . . . . . . . . 345 23.2.168MSK IPAR SOL FILTER KEEP BASIC . . . . . . . . . . . . . . . . . . . . . . 345 23.2.169MSK IPAR SOL FILTER KEEP RANGED . . . . . . . . . . . . . . . . . . . . . 345 23.2.170MSK IPAR SOL READ NAME WIDTH . . . . . . . . . . . . . . . . . . . . . . 346 23.2.171MSK IPAR SOL READ WIDTH . . . . . . . . . . . . . . . . . . . . . . . . . . . 346 23.2.172MSK IPAR SOLUTION CALLBACK . . . . . . . . . . . . . . . . . . . . . . . . 347 23.2.173MSK IPAR TIMING LEVEL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347
CONTENTS xv 23.2.174MSK IPAR WARNING LEVEL . . . . . . . . . . . . . . . . . . . . . . . . . . . 347 23.2.175MSK IPAR WRITE BAS CONSTRAINTS . . . . . . . . . . . . . . . . . . . . . 348 23.2.176MSK IPAR WRITE BAS HEAD . . . . . . . . . . . . . . . . . . . . . . . . . . . 348 23.2.177MSK IPAR WRITE BAS VARIABLES . . . . . . . . . . . . . . . . . . . . . . . 348 23.2.178MSK IPAR WRITE DATA COMPRESSED . . . . . . . . . . . . . . . . . . . . 349 23.2.179MSK IPAR WRITE DATA FORMAT . . . . . . . . . . . . . . . . . . . . . . . . 349 23.2.180MSK IPAR WRITE DATA PARAM . . . . . . . . . . . . . . . . . . . . . . . . . 349 23.2.181MSK IPAR WRITE FREE CON . . . . . . . . . . . . . . . . . . . . . . . . . . . 350 23.2.182MSK IPAR WRITE GENERIC NAMES . . . . . . . . . . . . . . . . . . . . . . 350 23.2.183MSK IPAR WRITE GENERIC NAMES IO . . . . . . . . . . . . . . . . . . . . 351 23.2.184MSK IPAR WRITE IGNORE INCOMPATIBLE CONIC ITEMS . . . . . . . . 351 23.2.185MSK IPAR WRITE IGNORE INCOMPATIBLE ITEMS . . . . . . . . . . . . . 351 23.2.186MSK IPAR WRITE IGNORE INCOMPATIBLE NL ITEMS . . . . . . . . . . . 352 23.2.187MSK IPAR WRITE IGNORE INCOMPATIBLE PSD ITEMS . . . . . . . . . . 352 23.2.188MSK IPAR WRITE INT CONSTRAINTS . . . . . . . . . . . . . . . . . . . . . 352 23.2.189MSK IPAR WRITE INT HEAD . . . . . . . . . . . . . . . . . . . . . . . . . . . 353 23.2.190MSK IPAR WRITE INT VARIABLES . . . . . . . . . . . . . . . . . . . . . . . 353 23.2.191MSK IPAR WRITE LP LINE WIDTH . . . . . . . . . . . . . . . . . . . . . . . 353 23.2.192MSK IPAR WRITE LP QUOTED NAMES . . . . . . . . . . . . . . . . . . . . 354 23.2.193MSK IPAR WRITE LP STRICT FORMAT . . . . . . . . . . . . . . . . . . . . 354 23.2.194MSK IPAR WRITE LP TERMS PER LINE . . . . . . . . . . . . . . . . . . . . 354 23.2.195MSK IPAR WRITE MPS INT . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355 23.2.196MSK IPAR WRITE PRECISION . . . . . . . . . . . . . . . . . . . . . . . . . . 355 23.2.197MSK IPAR WRITE SOL BARVARIABLES . . . . . . . . . . . . . . . . . . . . 355 23.2.198MSK IPAR WRITE SOL CONSTRAINTS . . . . . . . . . . . . . . . . . . . . . 356 23.2.199MSK IPAR WRITE SOL HEAD . . . . . . . . . . . . . . . . . . . . . . . . . . . 356 23.2.200MSK IPAR WRITE SOL IGNORE INVALID NAMES . . . . . . . . . . . . . . 356 23.2.201MSK IPAR WRITE SOL VARIABLES . . . . . . . . . . . . . . . . . . . . . . . 357 23.2.202MSK IPAR WRITE TASK INC SOL . . . . . . . . . . . . . . . . . . . . . . . . 357 23.2.203MSK IPAR WRITE XML MODE . . . . . . . . . . . . . . . . . . . . . . . . . . 357 23.3 MSKsparame: String parameter types . . . . . . . . . . . . . . . . . . . . . . . . . . . 358 23.3.1 MSK SPAR BAS SOL FILE NAME . . . . . . . . . . . . . . . . . . . . . . . . . 358 23.3.2 MSK SPAR DATA FILE NAME . . . . . . . . . . . . . . . . . . . . . . . . . . . 358 23.3.3 MSK SPAR DEBUG FILE NAME . . . . . . . . . . . . . . . . . . . . . . . . . . 358 23.3.4 MSK SPAR FEASREPAIR NAME PREFIX . . . . . . . . . . . . . . . . . . . . 359 23.3.5 MSK SPAR FEASREPAIR NAME SEPARATOR . . . . . . . . . . . . . . . . . 359 23.3.6 MSK SPAR FEASREPAIR NAME WSUMVIOL . . . . . . . . . . . . . . . . . . 359 23.3.7 MSK SPAR INT SOL FILE NAME . . . . . . . . . . . . . . . . . . . . . . . . . 360 23.3.8 MSK SPAR ITR SOL FILE NAME . . . . . . . . . . . . . . . . . . . . . . . . . 360 23.3.9 MSK SPAR MIO DEBUG STRING . . . . . . . . . . . . . . . . . . . . . . . . . 360 23.3.10 MSK SPAR PARAM COMMENT SIGN . . . . . . . . . . . . . . . . . . . . . . 361 23.3.11 MSK SPAR PARAM READ FILE NAME . . . . . . . . . . . . . . . . . . . . . 361 23.3.12 MSK SPAR PARAM WRITE FILE NAME . . . . . . . . . . . . . . . . . . . . . 361 23.3.13 MSK SPAR READ MPS BOU NAME . . . . . . . . . . . . . . . . . . . . . . . . 362 23.3.14 MSK SPAR READ MPS OBJ NAME . . . . . . . . . . . . . . . . . . . . . . . . 362 23.3.15 MSK SPAR READ MPS RAN NAME . . . . . . . . . . . . . . . . . . . . . . . . 362
Page 1 and 2: The MOSEK optimization toolbox for
Page 3 and 4: Contents 1 Changes and new features
Page 5 and 6: CONTENTS v 7.15.3 Speeding up the s
Page 7 and 8: CONTENTS vii 12.3 The mixed-integer
Page 9 and 10: CONTENTS ix 19.1.3 Bounds . . . . .
Page 11 and 12: CONTENTS xi 23.1.59 MSK DPAR PRESOL
Page 13: CONTENTS xiii 23.2.82 MSK IPAR MIO
Page 17 and 18: CONTENTS xvii 25.32 Problem data it
Page 19 and 20: Contact information Phone +45 3917
Page 21 and 22: License agreement Before using the
Page 23 and 24: Chapter 1 Changes and new features
Page 25 and 26: 1.4. API CHANGES 7 1.3.3 Mixed-inte
Page 27 and 28: Chapter 2 Introduction This manual
Page 29 and 30: Chapter 3 Supported MATLAB versions
Page 31 and 32: Chapter 4 Installation In order to
Page 33 and 34: 4.3. TROUBLESHOOTING 15 Search path
Page 35 and 36: Chapter 5 Getting support and help
Page 37 and 38: Chapter 6 MOSEK / MATLAB integratio
Page 39 and 40: Chapter 7 A guided tour 7.1 Introdu
Page 41 and 42: 7.4. LINEAR OPTIMIZATION 23 7.4.1 U
Page 43 and 44: 7.5. CONVEX QUADRATIC OPTIMIZATION
Page 45 and 46: 7.5. CONVEX QUADRATIC OPTIMIZATION
Page 47 and 48: 7.6. CONIC OPTIMIZATION 29 be vecto
Page 49 and 50: 7.6. CONIC OPTIMIZATION 31 minimize
Page 51 and 52: 7.6. CONIC OPTIMIZATION 33 • Quad
Page 53 and 54: 7.7. SEMIDEFINITE OPTIMIZATION 35 m
Page 55 and 56: 7.8. QUADRATICALLY CONSTRAINED OPTI
Page 57 and 58: 7.9. LINEAR LEAST SQUARES AND RELAT
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Page 61 and 62: 7.11. MORE ABOUT SOLVING LINEAR LEA
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7.11. MORE ABOUT SOLVING LINEAR LEA
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7.13. GEOMETRIC OPTIMIZATION 49 and
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7.13. GEOMETRIC OPTIMIZATION 51 27
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7.14. SEPARABLE CONVEX OPTIMIZATION
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7.15. MIXED-INTEGER OPTIMIZATION 55
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7.15. MIXED-INTEGER OPTIMIZATION 57
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7.16. SENSITIVITY ANALYSIS 59 24 25
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7.17. INSPECTING A PROBLEM 61 Const
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7.19. VIEWING THE TASK INFORMATION
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7.21. ADVANCED START (HOT-START) 65
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7.22. USING NAMES 71 7.22 Using nam
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7.24. USER CALL-BACK FUNCTIONS 73 U
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7.25. THE LICENSE SYSTEM 75 ture, t
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Chapter 8 Command reference After s
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8.1. DATA STRUCTURES 79 .blx Lower
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8.1. DATA STRUCTURES 81 must be sym
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8.1. DATA STRUCTURES 83 Field name
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8.1. DATA STRUCTURES 85 .type .sub
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8.1. DATA STRUCTURES 87 Comments: .
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8.1. DATA STRUCTURES 89 .rs bl Righ
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8.3. FUNCTIONS PROVIDED BY THE MOSE
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8.3. FUNCTIONS PROVIDED BY THE MOSE
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8.4. MATLAB OPTIMIZATION TOOLBOX CO
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Chapter 9 Case studies 9.1 Robust l
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9.1. ROBUST LINEAR OPTIMIZATION 109
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9.2. GEOMETRIC (POSYNOMIAL) OPTIMIZ
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Chapter 10 The optimizers for conti
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10.1. HOW AN OPTIMIZER WORKS 131 10
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10.2. LINEAR OPTIMIZATION 133 10.2.
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10.2. LINEAR OPTIMIZATION 135 Whene
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10.2. LINEAR OPTIMIZATION 137 10.2.
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10.2. LINEAR OPTIMIZATION 139 • R
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10.5. NONLINEAR CONVEX OPTIMIZATION
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10.6. SOLVING PROBLEMS IN PARALLEL
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Chapter 11 The solution summary All
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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 151 The
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12.7. UNDERSTANDING SOLUTION QUALIT
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Chapter 13 The solution summary for
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Chapter 14 The analyzers 14.1 The p
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14.1. THE PROBLEM ANALYZER 159 Cons
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14.2. ANALYZING INFEASIBLE PROBLEMS
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Chapter 15 Primal feasibility repai
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15.2. AUTOMATIC REPAIR 173 One way
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15.3. FEASIBILITY REPAIR IN MOSEK 1
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15.3. FEASIBILITY REPAIR IN MOSEK 1
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Chapter 16 Sensitivity analysis 16.
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16.4. SENSITIVITY ANALYSIS FOR LINE
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16.5. SENSITIVITY ANALYSIS IN THE M
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Chapter 17 Problem formulation and
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17.1. LINEAR OPTIMIZATION 195 be a
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17.2. CONIC QUADRATIC OPTIMIZATION
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17.2. CONIC QUADRATIC OPTIMIZATION
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17.3. SEMIDEFINITE OPTIMIZATION 201
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17.5. GENERAL CONVEX OPTIMIZATION 2
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17.5. GENERAL CONVEX OPTIMIZATION 2
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Chapter 18 The MPS file format MOSE
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18.1. MPS FILE STRUCTURE 209 Extens
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18.1. MPS FILE STRUCTURE 211 [vname
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18.1. MPS FILE STRUCTURE 213 Field
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18.1. MPS FILE STRUCTURE 215 Next d
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18.2. INTEGER VARIABLES 217 18.2 In
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Chapter 19 The LP file format MOSEK
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19.1. THE SECTIONS 221 x1 * x2 Ther
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19.2. LP FORMAT PECULIARITIES 223 1
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19.3. THE STRICT LP FORMAT 225 MSK
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Chapter 20 The OPF format The Optim
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20.2. THE FILE FORMAT 229 [con ’c
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20.2. THE FILE FORMAT 231 - ‘NEAR
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20.4. WRITING OPF FILES FROM MOSEK
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20.5. EXAMPLES 235 [/hints] [variab
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20.5. EXAMPLES 237 x1 x2 [/integer]
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Chapter 21 The Task format The Task
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Chapter 22 The XML (OSiL) format MO
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Chapter 23 Parameters Parameters gr
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245 • MSK SPAR ITR SOL FILE NAME.
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247 • MSK DPAR INTPNT NL TOL REL
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249 • MSK IPAR LOG MIO. Controls
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251 • MSK DPAR INTPNT NL MERIT BA
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253 • MSK IPAR INFEAS PREFER PRIM
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255 • MSK IPAR SIM SAVE LU. Contr
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23.1. MSKDPARAME: DOUBLE PARAMETERS
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23.2. MSKIPARAME: INTEGER PARAMETER
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23.3. MSKSPARAME: STRING PARAMETER
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Chapter 24 Response codes Response
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369 MSK RES ERR CON Q NOT PSD The q
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371 MSK RES ERR GLOBAL INV CONIC PR
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373 MSK RES ERR INV MARKJ Invalid v
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375 MSK RES ERR INVALID FORMAT TYPE
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377 MSK RES ERR LICENSE NO SERVER S
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379 MSK RES ERR MIO NO OPTIMIZER No
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381 MSK RES ERR NAME MAX LEN A name
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383 MSK RES ERR NUMCONLIM Maximum n
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385 MSK RES ERR QCON UPPER TRIANGLE
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387 MSK RES ERR SYM MAT INVALID COL
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389 MSK RES ERR USER NLO FUNC The u
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391 MSK RES WRN ANA ALMOST INT BOUN
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393 MSK RES WRN MIO INFEASIBLE FINA
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395 MSK RES WRN WRITE DISCARDED CFI
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Chapter 25 API constants 25.1 Const
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25.5. PROGRESS CALL-BACK CODES 399
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25.6. TYPES OF CONVEXITY CHECKS. 40
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25.10. DOUBLE INFORMATION ITEMS 409
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25.10. DOUBLE INFORMATION ITEMS 411
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25.11. FEASIBILITY REPAIR TYPES 413
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25.13. INTEGER INFORMATION ITEMS. 4
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25.17. LANGUAGE SELECTION CONSTANTS
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25.22. MIXED-INTEGER NODE SELECTION
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25.29. ORDERING STRATEGIES 425 MSK
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25.34. PROBLEM STATUS KEYS 427 MSK
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25.38. SENSITIVITY TYPES 429 MSK SC
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25.44. SOLUTION ITEMS 431 MSK SIM S
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25.46. SOLUTION TYPES 433 25.46 Sol
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25.52. INTEGER VALUES 435 25.52 Int
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Chapter 26 Problem analyzer example
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26.2. ARKI001 439 2 476 45.42 48.19
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26.4. PROBLEM WITH BOTH LINEAR AND
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Bibliography [1] Chvátal, V.. Line
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Index basis identification, 136 bin
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INDEX 447 MSK RES ERR DUPLICATE CON
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INDEX 449 MSK RES ERR MPS INVALID O
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INDEX 451 MSK RES ERR XML INVALID P
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