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

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xii CONTENTS 23.2.36 MSK IPAR INTPNT SOLVE FORM . . . . . . . . . . . . . . . . . . . . . . . . 294 23.2.37 MSK IPAR INTPNT STARTING POINT . . . . . . . . . . . . . . . . . . . . . . 295 23.2.38 MSK IPAR LIC TRH EXPIRY WRN . . . . . . . . . . . . . . . . . . . . . . . . 295 23.2.39 MSK IPAR LICENSE ALLOW OVERUSE . . . . . . . . . . . . . . . . . . . . . 296 23.2.40 MSK IPAR LICENSE DEBUG . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296 23.2.41 MSK IPAR LICENSE PAUSE TIME . . . . . . . . . . . . . . . . . . . . . . . . 296 23.2.42 MSK IPAR LICENSE SUPPRESS EXPIRE WRNS . . . . . . . . . . . . . . . . 297 23.2.43 MSK IPAR LICENSE WAIT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297 23.2.44 MSK IPAR LOG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297 23.2.45 MSK IPAR LOG BI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 298 23.2.46 MSK IPAR LOG BI FREQ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 298 23.2.47 MSK IPAR LOG CHECK CONVEXITY . . . . . . . . . . . . . . . . . . . . . . 299 23.2.48 MSK IPAR LOG CONCURRENT . . . . . . . . . . . . . . . . . . . . . . . . . . 299 23.2.49 MSK IPAR LOG CUT SECOND OPT . . . . . . . . . . . . . . . . . . . . . . . 299 23.2.50 MSK IPAR LOG EXPAND . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300 23.2.51 MSK IPAR LOG FACTOR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300 23.2.52 MSK IPAR LOG FEAS REPAIR . . . . . . . . . . . . . . . . . . . . . . . . . . 301 23.2.53 MSK IPAR LOG FILE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301 23.2.54 MSK IPAR LOG HEAD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301 23.2.55 MSK IPAR LOG INFEAS ANA . . . . . . . . . . . . . . . . . . . . . . . . . . . 302 23.2.56 MSK IPAR LOG INTPNT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302 23.2.57 MSK IPAR LOG MIO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302 23.2.58 MSK IPAR LOG MIO FREQ . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303 23.2.59 MSK IPAR LOG NONCONVEX . . . . . . . . . . . . . . . . . . . . . . . . . . . 303 23.2.60 MSK IPAR LOG OPTIMIZER . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303 23.2.61 MSK IPAR LOG ORDER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304 23.2.62 MSK IPAR LOG PARAM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304 23.2.63 MSK IPAR LOG PRESOLVE . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304 23.2.64 MSK IPAR LOG RESPONSE . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305 23.2.65 MSK IPAR LOG SENSITIVITY . . . . . . . . . . . . . . . . . . . . . . . . . . . 305 23.2.66 MSK IPAR LOG SENSITIVITY OPT . . . . . . . . . . . . . . . . . . . . . . . . 305 23.2.67 MSK IPAR LOG SIM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306 23.2.68 MSK IPAR LOG SIM FREQ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306 23.2.69 MSK IPAR LOG SIM MINOR . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306 23.2.70 MSK IPAR LOG SIM NETWORK FREQ . . . . . . . . . . . . . . . . . . . . . 307 23.2.71 MSK IPAR LOG STORAGE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307 23.2.72 MSK IPAR MAX NUM WARNINGS . . . . . . . . . . . . . . . . . . . . . . . . 307 23.2.73 MSK IPAR MIO BRANCH DIR . . . . . . . . . . . . . . . . . . . . . . . . . . . 308 23.2.74 MSK IPAR MIO BRANCH PRIORITIES USE . . . . . . . . . . . . . . . . . . . 308 23.2.75 MSK IPAR MIO CONSTRUCT SOL . . . . . . . . . . . . . . . . . . . . . . . . 308 23.2.76 MSK IPAR MIO CONT SOL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309 23.2.77 MSK IPAR MIO CUT LEVEL ROOT . . . . . . . . . . . . . . . . . . . . . . . . 309 23.2.78 MSK IPAR MIO CUT LEVEL TREE . . . . . . . . . . . . . . . . . . . . . . . . 310 23.2.79 MSK IPAR MIO FEASPUMP LEVEL . . . . . . . . . . . . . . . . . . . . . . . 310 23.2.80 MSK IPAR MIO HEURISTIC LEVEL . . . . . . . . . . . . . . . . . . . . . . . 311 23.2.81 MSK IPAR MIO HOTSTART . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311
CONTENTS xiii 23.2.82 MSK IPAR MIO KEEP BASIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312 23.2.83 MSK IPAR MIO LOCAL BRANCH NUMBER . . . . . . . . . . . . . . . . . . 312 23.2.84 MSK IPAR MIO MAX NUM BRANCHES . . . . . . . . . . . . . . . . . . . . . 312 23.2.85 MSK IPAR MIO MAX NUM RELAXS . . . . . . . . . . . . . . . . . . . . . . . 313 23.2.86 MSK IPAR MIO MAX NUM SOLUTIONS . . . . . . . . . . . . . . . . . . . . . 313 23.2.87 MSK IPAR MIO MODE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314 23.2.88 MSK IPAR MIO MT USER CB . . . . . . . . . . . . . . . . . . . . . . . . . . . 314 23.2.89 MSK IPAR MIO NODE OPTIMIZER . . . . . . . . . . . . . . . . . . . . . . . . 314 23.2.90 MSK IPAR MIO NODE SELECTION . . . . . . . . . . . . . . . . . . . . . . . . 315 23.2.91 MSK IPAR MIO OPTIMIZER MODE . . . . . . . . . . . . . . . . . . . . . . . 316 23.2.92 MSK IPAR MIO PRESOLVE AGGREGATE . . . . . . . . . . . . . . . . . . . . 316 23.2.93 MSK IPAR MIO PRESOLVE PROBING . . . . . . . . . . . . . . . . . . . . . . 316 23.2.94 MSK IPAR MIO PRESOLVE USE . . . . . . . . . . . . . . . . . . . . . . . . . . 317 23.2.95 MSK IPAR MIO ROOT OPTIMIZER . . . . . . . . . . . . . . . . . . . . . . . . 317 23.2.96 MSK IPAR MIO STRONG BRANCH . . . . . . . . . . . . . . . . . . . . . . . . 318 23.2.97 MSK IPAR MIO USE MULTITHREADED OPTIMIZER . . . . . . . . . . . . . 318 23.2.98 MSK IPAR MT SPINCOUNT . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318 23.2.99 MSK IPAR NONCONVEX MAX ITERATIONS . . . . . . . . . . . . . . . . . . 319 23.2.100MSK IPAR NUM THREADS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319 23.2.101MSK IPAR OPF MAX TERMS PER LINE . . . . . . . . . . . . . . . . . . . . 319 23.2.102MSK IPAR OPF WRITE HEADER . . . . . . . . . . . . . . . . . . . . . . . . . 320 23.2.103MSK IPAR OPF WRITE HINTS . . . . . . . . . . . . . . . . . . . . . . . . . . 320 23.2.104MSK IPAR OPF WRITE PARAMETERS . . . . . . . . . . . . . . . . . . . . . 320 23.2.105MSK IPAR OPF WRITE PROBLEM . . . . . . . . . . . . . . . . . . . . . . . . 321 23.2.106MSK IPAR OPF WRITE SOL BAS . . . . . . . . . . . . . . . . . . . . . . . . . 321 23.2.107MSK IPAR OPF WRITE SOL ITG . . . . . . . . . . . . . . . . . . . . . . . . . 321 23.2.108MSK IPAR OPF WRITE SOL ITR . . . . . . . . . . . . . . . . . . . . . . . . . 322 23.2.109MSK IPAR OPF WRITE SOLUTIONS . . . . . . . . . . . . . . . . . . . . . . . 322 23.2.110MSK IPAR OPTIMIZER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323 23.2.111MSK IPAR PARAM READ CASE NAME . . . . . . . . . . . . . . . . . . . . . 323 23.2.112MSK IPAR PARAM READ IGN ERROR . . . . . . . . . . . . . . . . . . . . . 324 23.2.113MSK IPAR PRESOLVE ELIM FILL . . . . . . . . . . . . . . . . . . . . . . . . 324 23.2.114MSK IPAR PRESOLVE ELIMINATOR MAX NUM TRIES . . . . . . . . . . . 324 23.2.115MSK IPAR PRESOLVE ELIMINATOR USE . . . . . . . . . . . . . . . . . . . . 325 23.2.116MSK IPAR PRESOLVE LEVEL . . . . . . . . . . . . . . . . . . . . . . . . . . . 325 23.2.117MSK IPAR PRESOLVE LINDEP ABS WORK TRH . . . . . . . . . . . . . . . 325 23.2.118MSK IPAR PRESOLVE LINDEP REL WORK TRH . . . . . . . . . . . . . . . 326 23.2.119MSK IPAR PRESOLVE LINDEP USE . . . . . . . . . . . . . . . . . . . . . . . 326 23.2.120MSK IPAR PRESOLVE MAX NUM REDUCTIONS . . . . . . . . . . . . . . . 326 23.2.121MSK IPAR PRESOLVE USE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327 23.2.122MSK IPAR PRIMAL REPAIR OPTIMIZER . . . . . . . . . . . . . . . . . . . . 327 23.2.123MSK IPAR QO SEPARABLE REFORMULATION . . . . . . . . . . . . . . . . 328 23.2.124MSK IPAR READ ANZ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328 23.2.125MSK IPAR READ CON . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328 23.2.126MSK IPAR READ CONE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329 23.2.127MSK IPAR READ DATA COMPRESSED . . . . . . . . . . . . . . . . . . . . . 329
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: CONTENTS xi 23.1.59 MSK DPAR PRESOL
Page 15 and 16: CONTENTS xv 23.2.174MSK IPAR WARNIN
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
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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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