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

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x CONTENTS 23.1.13 MSK DPAR DATA TOL QIJ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261 23.1.14 MSK DPAR DATA TOL X . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261 23.1.15 MSK DPAR FEASREPAIR TOL . . . . . . . . . . . . . . . . . . . . . . . . . . 262 23.1.16 MSK DPAR INTPNT CO TOL DFEAS . . . . . . . . . . . . . . . . . . . . . . 262 23.1.17 MSK DPAR INTPNT CO TOL INFEAS . . . . . . . . . . . . . . . . . . . . . . 263 23.1.18 MSK DPAR INTPNT CO TOL MU RED . . . . . . . . . . . . . . . . . . . . . 263 23.1.19 MSK DPAR INTPNT CO TOL NEAR REL . . . . . . . . . . . . . . . . . . . . 263 23.1.20 MSK DPAR INTPNT CO TOL PFEAS . . . . . . . . . . . . . . . . . . . . . . . 264 23.1.21 MSK DPAR INTPNT CO TOL REL GAP . . . . . . . . . . . . . . . . . . . . . 264 23.1.22 MSK DPAR INTPNT NL MERIT BAL . . . . . . . . . . . . . . . . . . . . . . . 264 23.1.23 MSK DPAR INTPNT NL TOL DFEAS . . . . . . . . . . . . . . . . . . . . . . . 265 23.1.24 MSK DPAR INTPNT NL TOL MU RED . . . . . . . . . . . . . . . . . . . . . . 265 23.1.25 MSK DPAR INTPNT NL TOL NEAR REL . . . . . . . . . . . . . . . . . . . . 265 23.1.26 MSK DPAR INTPNT NL TOL PFEAS . . . . . . . . . . . . . . . . . . . . . . . 266 23.1.27 MSK DPAR INTPNT NL TOL REL GAP . . . . . . . . . . . . . . . . . . . . . 266 23.1.28 MSK DPAR INTPNT NL TOL REL STEP . . . . . . . . . . . . . . . . . . . . . 266 23.1.29 MSK DPAR INTPNT TOL DFEAS . . . . . . . . . . . . . . . . . . . . . . . . . 267 23.1.30 MSK DPAR INTPNT TOL DSAFE . . . . . . . . . . . . . . . . . . . . . . . . . 267 23.1.31 MSK DPAR INTPNT TOL INFEAS . . . . . . . . . . . . . . . . . . . . . . . . 267 23.1.32 MSK DPAR INTPNT TOL MU RED . . . . . . . . . . . . . . . . . . . . . . . . 268 23.1.33 MSK DPAR INTPNT TOL PATH . . . . . . . . . . . . . . . . . . . . . . . . . . 268 23.1.34 MSK DPAR INTPNT TOL PFEAS . . . . . . . . . . . . . . . . . . . . . . . . . 268 23.1.35 MSK DPAR INTPNT TOL PSAFE . . . . . . . . . . . . . . . . . . . . . . . . . 269 23.1.36 MSK DPAR INTPNT TOL REL GAP . . . . . . . . . . . . . . . . . . . . . . . 269 23.1.37 MSK DPAR INTPNT TOL REL STEP . . . . . . . . . . . . . . . . . . . . . . . 269 23.1.38 MSK DPAR INTPNT TOL STEP SIZE . . . . . . . . . . . . . . . . . . . . . . . 270 23.1.39 MSK DPAR LOWER OBJ CUT . . . . . . . . . . . . . . . . . . . . . . . . . . . 270 23.1.40 MSK DPAR LOWER OBJ CUT FINITE TRH . . . . . . . . . . . . . . . . . . 270 23.1.41 MSK DPAR MIO DISABLE TERM TIME . . . . . . . . . . . . . . . . . . . . . 271 23.1.42 MSK DPAR MIO HEURISTIC TIME . . . . . . . . . . . . . . . . . . . . . . . . 271 23.1.43 MSK DPAR MIO MAX TIME . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272 23.1.44 MSK DPAR MIO MAX TIME APRX OPT . . . . . . . . . . . . . . . . . . . . 272 23.1.45 MSK DPAR MIO NEAR TOL ABS GAP . . . . . . . . . . . . . . . . . . . . . . 273 23.1.46 MSK DPAR MIO NEAR TOL REL GAP . . . . . . . . . . . . . . . . . . . . . . 273 23.1.47 MSK DPAR MIO REL ADD CUT LIMITED . . . . . . . . . . . . . . . . . . . 274 23.1.48 MSK DPAR MIO REL GAP CONST . . . . . . . . . . . . . . . . . . . . . . . . 274 23.1.49 MSK DPAR MIO TOL ABS GAP . . . . . . . . . . . . . . . . . . . . . . . . . . 274 23.1.50 MSK DPAR MIO TOL ABS RELAX INT . . . . . . . . . . . . . . . . . . . . . 275 23.1.51 MSK DPAR MIO TOL FEAS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275 23.1.52 MSK DPAR MIO TOL REL DUAL BOUND IMPROVEMENT . . . . . . . . . 275 23.1.53 MSK DPAR MIO TOL REL GAP . . . . . . . . . . . . . . . . . . . . . . . . . . 276 23.1.54 MSK DPAR MIO TOL REL RELAX INT . . . . . . . . . . . . . . . . . . . . . 276 23.1.55 MSK DPAR MIO TOL X . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276 23.1.56 MSK DPAR NONCONVEX TOL FEAS . . . . . . . . . . . . . . . . . . . . . . 277 23.1.57 MSK DPAR NONCONVEX TOL OPT . . . . . . . . . . . . . . . . . . . . . . . 277 23.1.58 MSK DPAR OPTIMIZER MAX TIME . . . . . . . . . . . . . . . . . . . . . . . 277
CONTENTS xi 23.1.59 MSK DPAR PRESOLVE TOL ABS LINDEP . . . . . . . . . . . . . . . . . . . 278 23.1.60 MSK DPAR PRESOLVE TOL AIJ . . . . . . . . . . . . . . . . . . . . . . . . . 278 23.1.61 MSK DPAR PRESOLVE TOL REL LINDEP . . . . . . . . . . . . . . . . . . . 278 23.1.62 MSK DPAR PRESOLVE TOL S . . . . . . . . . . . . . . . . . . . . . . . . . . . 279 23.1.63 MSK DPAR PRESOLVE TOL X . . . . . . . . . . . . . . . . . . . . . . . . . . 279 23.1.64 MSK DPAR QCQO REFORMULATE REL DROP TOL . . . . . . . . . . . . . 279 23.1.65 MSK DPAR SIM LU TOL REL PIV . . . . . . . . . . . . . . . . . . . . . . . . 280 23.1.66 MSK DPAR SIMPLEX ABS TOL PIV . . . . . . . . . . . . . . . . . . . . . . . 280 23.1.67 MSK DPAR UPPER OBJ CUT . . . . . . . . . . . . . . . . . . . . . . . . . . . 280 23.1.68 MSK DPAR UPPER OBJ CUT FINITE TRH . . . . . . . . . . . . . . . . . . . 281 23.2 MSKiparame: Integer parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281 23.2.1 MSK IPAR ALLOC ADD QNZ . . . . . . . . . . . . . . . . . . . . . . . . . . . 281 23.2.2 MSK IPAR ANA SOL BASIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282 23.2.3 MSK IPAR ANA SOL PRINT VIOLATED . . . . . . . . . . . . . . . . . . . . . 282 23.2.4 MSK IPAR AUTO SORT A BEFORE OPT . . . . . . . . . . . . . . . . . . . . 282 23.2.5 MSK IPAR AUTO UPDATE SOL INFO . . . . . . . . . . . . . . . . . . . . . . 283 23.2.6 MSK IPAR BASIS SOLVE USE PLUS ONE . . . . . . . . . . . . . . . . . . . . 283 23.2.7 MSK IPAR BI CLEAN OPTIMIZER . . . . . . . . . . . . . . . . . . . . . . . . 283 23.2.8 MSK IPAR BI IGNORE MAX ITER . . . . . . . . . . . . . . . . . . . . . . . . 284 23.2.9 MSK IPAR BI IGNORE NUM ERROR . . . . . . . . . . . . . . . . . . . . . . . 284 23.2.10 MSK IPAR BI MAX ITERATIONS . . . . . . . . . . . . . . . . . . . . . . . . . 285 23.2.11 MSK IPAR CACHE LICENSE . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285 23.2.12 MSK IPAR CHECK CONVEXITY . . . . . . . . . . . . . . . . . . . . . . . . . 286 23.2.13 MSK IPAR COMPRESS STATFILE . . . . . . . . . . . . . . . . . . . . . . . . . 286 23.2.14 MSK IPAR CONCURRENT NUM OPTIMIZERS . . . . . . . . . . . . . . . . . 286 23.2.15 MSK IPAR CONCURRENT PRIORITY DUAL SIMPLEX . . . . . . . . . . . . 287 23.2.16 MSK IPAR CONCURRENT PRIORITY FREE SIMPLEX . . . . . . . . . . . . 287 23.2.17 MSK IPAR CONCURRENT PRIORITY INTPNT . . . . . . . . . . . . . . . . 287 23.2.18 MSK IPAR CONCURRENT PRIORITY PRIMAL SIMPLEX . . . . . . . . . . 288 23.2.19 MSK IPAR FEASREPAIR OPTIMIZE . . . . . . . . . . . . . . . . . . . . . . . 288 23.2.20 MSK IPAR INFEAS GENERIC NAMES . . . . . . . . . . . . . . . . . . . . . . 288 23.2.21 MSK IPAR INFEAS PREFER PRIMAL . . . . . . . . . . . . . . . . . . . . . . 289 23.2.22 MSK IPAR INFEAS REPORT AUTO . . . . . . . . . . . . . . . . . . . . . . . . 289 23.2.23 MSK IPAR INFEAS REPORT LEVEL . . . . . . . . . . . . . . . . . . . . . . . 289 23.2.24 MSK IPAR INTPNT BASIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290 23.2.25 MSK IPAR INTPNT DIFF STEP . . . . . . . . . . . . . . . . . . . . . . . . . . 290 23.2.26 MSK IPAR INTPNT FACTOR DEBUG LVL . . . . . . . . . . . . . . . . . . . 291 23.2.27 MSK IPAR INTPNT FACTOR METHOD . . . . . . . . . . . . . . . . . . . . . 291 23.2.28 MSK IPAR INTPNT HOTSTART . . . . . . . . . . . . . . . . . . . . . . . . . . 291 23.2.29 MSK IPAR INTPNT MAX ITERATIONS . . . . . . . . . . . . . . . . . . . . . 292 23.2.30 MSK IPAR INTPNT MAX NUM COR . . . . . . . . . . . . . . . . . . . . . . . 292 23.2.31 MSK IPAR INTPNT MAX NUM REFINEMENT STEPS . . . . . . . . . . . . 292 23.2.32 MSK IPAR INTPNT OFF COL TRH . . . . . . . . . . . . . . . . . . . . . . . . 293 23.2.33 MSK IPAR INTPNT ORDER METHOD . . . . . . . . . . . . . . . . . . . . . . 293 23.2.34 MSK IPAR INTPNT REGULARIZATION USE . . . . . . . . . . . . . . . . . . 294 23.2.35 MSK IPAR INTPNT SCALING . . . . . . . . . . . . . . . . . . . . . . . . . . . 294
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: CONTENTS ix 19.1.3 Bounds . . . . .
Page 13 and 14: CONTENTS xiii 23.2.82 MSK IPAR MIO
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
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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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7.13. 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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