The MOSEK command line tool Version 7.0 (Revision 141)

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46 CHAPTER 5. THE OPTIMIZERS FOR CONTINUOUS PROBLEMS Parameter name MSK DPAR INTPNT NL TOL PFEAS MSK DPAR INTPNT NL TOL DFEAS MSK DPAR INTPNT NL TOL REL GAP MSK DPAR INTPNT TOL INFEAS MSK DPAR INTPNT NL TOL MU RED Purpose Controls primal feasibility Controls dual feasibility Controls relative gap Controls when the problem is declared infeasible Controls when the complementarity is reduced enough Table 5.3: Parameters employed in termination criteria. In this case the bounds f(x) = 1 x + 1 1 − x . (5.6) 0 ≤ x ≤ 1 will not guarantee that MOSEK only evaluates the function for x between 0 and 1 . To force MOSEK to strictly satisfy both bounds on ranged variables set the parameter MSK IPAR INTPNT STARTING POINT to MSK STARTING POINT SATISFY BOUNDS. For efficiency reasons it may be better to reformulate the problem than to force MOSEK to observe ranged bounds strictly. For instance, (5.6) can be reformulated as follows f(x) = 1 x + 1 y 0 = 1 − x − y 0 ≤ x 0 ≤ y. 5.5.1.3 Interior-point termination criteria The parameters controlling when the general convex interior-point optimizer terminates are shown in Table 5.3. 5.6 Solving problems in parallel If a computer has multiple CPUs, or has a CPU with multiple cores, it is possible for MOSEK to take advantage of this to speed up solution times. 5.6.1 Thread safety The MOSEK API is thread-safe provided that a task is only modified or accessed from one thread at any given time — accessing two separate tasks from two separate threads at the same time is safe. Sharing an environment between threads is safe.
5.6. SOLVING PROBLEMS IN PARALLEL 47 5.6.2 The parallelized interior-point optimizer The interior-point optimizer is capable of using multiple CPUs or cores. This implies that whenever the MOSEK interior-point optimizer solves an optimization problem, it will try to divide the work so that each core gets a share of the work. The user decides how many coress MOSEK should exploit. It is not always possible to divide the work equally, and often parts of the computations and the coordination of the work is processed sequentially, even if several cores are present. Therefore, the speed-up obtained when using multiple cores is highly problem dependent. However, as a rule of thumb, if the problem solves very quickly, i.e. in less than 60 seconds, it is not advantageous to use the parallel option. The MSK IPAR NUM THREADS parameter sets the number of threads (and therefore the number of cores) that the interior point optimizer will use. 5.6.3 The concurrent optimizer An alternative to the parallel interior-point optimizer is the concurrent optimizer. The idea of the concurrent optimizer is to run multiple optimizers on the same problem concurrently, for instance, it allows you to apply the interior-point and the dual simplex optimizers to a linear optimization problem concurrently. The concurrent optimizer terminates when the first of the applied optimizers has terminated successfully, and it reports the solution of the fastest optimizer. In that way a new optimizer has been created which essentially performs as the fastest of the interior-point and the dual simplex optimizers. Hence, the concurrent optimizer is the best one to use if there are multiple optimizers available in MOSEK for the problem and you cannot say beforehand which one will be faster. Note in particular that any solution present in the task will also be used for hot-starting the simplex algorithms. One possible scenario would therefore be running a hot-start dual simplex in parallel with interior point, taking advantage of both the stability of the interior-point method and the ability of the simplex method to use an initial solution. By setting the MSK IPAR OPTIMIZER parameter to MSK OPTIMIZER CONCURRENT the concurrent optimizer chosen. The number of optimizers used in parallel is determined by the MSK IPAR CONCURRENT NUM OPTIMIZERS. parameter. Moreover, the optimizers are selected according to a preassigned priority with optimizers having the highest priority being selected first. The default priority for each optimizer is shown in Table 5.6.3. For example, setting the MSK IPAR CONCURRENT NUM OPTIMIZERS parameter to 2 tells the concurrent optimizer to the apply the two optimizers with highest priorities: In the default case that means the interior-point optimizer and one of the simplex optimizers.
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The MOSEK command line tool. Versio
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Contents 1 Changes and new features
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CONTENTS v 6.5 Termination criterio
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CONTENTS vii 9.1.56 MSK DPAR NONCON
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CONTENTS ix 9.2.79 MSK IPAR MIO FEA
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Page 13 and 14: CONTENTS xiii 11.29 Ordering strate
Page 15 and 16: CONTENTS xv 18.2 arki001 . . . . .
Page 17 and 18: Contact information Phone +45 3917
Page 19 and 20: License agreement Before using the
Page 21 and 22: Chapter 1 Changes and new features
Page 23 and 24: 1.4. OPTIMIZATION TOOLBOX FOR MATLA
Page 25 and 26: Chapter 2 What is MOSEK MOSEK is a
Page 27 and 28: Chapter 3 MOSEK and AMPL AMPL is a
Page 29 and 30: 3.6. CONSTRAINT AND VARIABLE NAMES
Page 31 and 32: 3.8. HOT-START 15 Linear dependency
Page 33 and 34: 3.10. SENSITIVITY ANALYSIS 17 • .
Page 35 and 36: Chapter 4 Problem formulation and s
Page 37 and 38: 4.1. LINEAR OPTIMIZATION 21 be a pr
Page 39 and 40: 4.2. CONIC QUADRATIC OPTIMIZATION 2
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Page 43 and 44: 4.3. SEMIDEFINITE OPTIMIZATION 27 4
Page 45 and 46: 4.5. GENERAL CONVEX OPTIMIZATION 29
Page 47 and 48: 4.5. GENERAL CONVEX OPTIMIZATION 31
Page 49 and 50: Chapter 5 The optimizers for contin
Page 51 and 52: 5.1. HOW AN OPTIMIZER WORKS 35 5.1.
Page 53 and 54: 5.2. LINEAR OPTIMIZATION 37 5.2.2 T
Page 55 and 56: 5.2. LINEAR OPTIMIZATION 39 Wheneve
Page 57 and 58: 5.2. LINEAR OPTIMIZATION 41 5.2.2.3
Page 59 and 60: 5.2. LINEAR OPTIMIZATION 43 • Rai
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Page 73 and 74: Chapter 7 The analyzers 7.1 The pro
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Page 77 and 78: 7.2. ANALYZING INFEASIBLE PROBLEMS
Page 87 and 88: Chapter 8 Sensitivity analysis 8.1
Page 89 and 90: 8.4. SENSITIVITY ANALYSIS FOR LINEA
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Page 95 and 96: Chapter 9 Parameters Parameters gro
Page 97 and 98: 81 • MSK SPAR ITR SOL FILE NAME.
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9.1. MSKDPARAME: DOUBLE PARAMETERS
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9.2. MSKIPARAME: INTEGER PARAMETERS
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9.3. MSKSPARAME: STRING PARAMETER T
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Chapter 10 Response codes Response
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205 MSK RES ERR CON Q NOT PSD The q
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207 MSK RES ERR GLOBAL INV CONIC PR
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209 MSK RES ERR INV MARKJ Invalid v
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211 MSK RES ERR INVALID FORMAT TYPE
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213 MSK RES ERR LICENSE NO SERVER S
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215 MSK RES ERR MIO NO OPTIMIZER No
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217 MSK RES ERR NAME MAX LEN A name
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219 MSK RES ERR NUMCONLIM Maximum n
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221 MSK RES ERR QCON UPPER TRIANGLE
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223 MSK RES ERR SYM MAT INVALID COL
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225 MSK RES ERR USER NLO FUNC The u
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227 MSK RES WRN ANA ALMOST INT BOUN
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229 MSK RES WRN MIO INFEASIBLE FINA
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231 MSK RES WRN WRITE DISCARDED CFI
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Chapter 11 API constants 11.1 Const
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11.5. PROGRESS CALL-BACK CODES 235
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11.6. TYPES OF CONVEXITY CHECKS. 24
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11.10. DOUBLE INFORMATION ITEMS 245
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11.10. DOUBLE INFORMATION ITEMS 247
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11.11. FEASIBILITY REPAIR TYPES 249
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11.13. INTEGER INFORMATION ITEMS. 2
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11.17. LANGUAGE SELECTION CONSTANTS
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11.22. MIXED-INTEGER NODE SELECTION
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11.29. ORDERING STRATEGIES 261 MSK
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11.34. PROBLEM STATUS KEYS 263 MSK
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11.38. SENSITIVITY TYPES 265 MSK SC
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11.44. SOLUTION ITEMS 267 MSK SIM S
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11.46. SOLUTION TYPES 269 11.46 Sol
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11.52. INTEGER VALUES 271 11.52 Int
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Chapter 12 MOSEK Command line tool
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12.3. THE PARAMETER FILE 275 -min F
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Chapter 13 The MPS file format MOSE
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13.1. MPS FILE STRUCTURE 279 Extens
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13.1. MPS FILE STRUCTURE 281 [vname
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13.1. MPS FILE STRUCTURE 283 Field
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13.1. MPS FILE STRUCTURE 285 Next d
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13.2. INTEGER VARIABLES 287 13.2 In
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Chapter 14 The LP file format MOSEK
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14.1. THE SECTIONS 291 x1 * x2 Ther
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14.2. LP FORMAT PECULIARITIES 293 1
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14.3. THE STRICT LP FORMAT 295 MSK
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Chapter 15 The OPF format The Optim
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15.2. THE FILE FORMAT 299 [con ’c
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15.2. THE FILE FORMAT 301 - ‘NEAR
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15.4. WRITING OPF FILES FROM MOSEK
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15.5. EXAMPLES 305 [/hints] [variab
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15.5. EXAMPLES 307 x1 x2 [/integer]
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Chapter 16 The XML (OSiL) format MO
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Chapter 17 The solution file format
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17.2. THE INTEGER SOLUTION FILE 313
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Chapter 18 Problem analyzer example
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18.2. ARKI001 317 2 476 45.42 48.19
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18.4. PROBLEM WITH BOTH LINEAR AND
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Bibliography [1] R. Fourer and D. M
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Index AMPL outlev, 13 wantsol, 13 a
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INDEX 325 MSK RES ERR FEASREPAIR IN
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INDEX 327 MSK RES ERR MPS NULL VAR
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INDEX 329 MSK RES TRM MAX TIME, 226
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