The MOSEK command line tool Version 7.0 (Revision 141)

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62 CHAPTER 7. THE ANALYZERS Supply Demand 200 Plant 1 1 2 Store 1 1100 1000 Plant 2 1 Store 2 200 5 Store 3 500 1000 Plant 3 2 1 2 Store 4 500 Figure 7.1: Supply, demand and cost of transportation. 7.2.1 Example: Primal infeasibility A problem is said to be primal infeasible if no solution exists that satisfy all the constraints of the problem. As an example of a primal infeasible problem consider the problem of minimizing the cost of transportation between a number of production plants and stores: Each plant produces a fixed number of goods, and each store has a fixed demand that must be met. Supply, demand and cost of transportation per unit are given in figure 7.1. The problem represented in figure 7.1 is infeasible, since the total demand exceeds the total supply 2300 = 1100 + 200 + 500 + 500 2200 = 200 + 1000 + 1000 If we denote the number of transported goods from plant i to store j by x ij , the problem can be formulated as the LP:
7.2. ANALYZING INFEASIBLE PROBLEMS 63 minimize x 11 + 2x 12 + 5x 23 + 2x 24 + x 31 + 2x 33 + x 34 subject to x 11 + x 12 ≤ 200, x 23 + x 24 ≤ 1000, x 31 + x 33 + x 34 ≤ 1000, x 11 + x 31 = 1100, x 12 = 200, x 23 + x 33 = 500, x 24 + x 34 = 500, x ij ≥ 0. (7.1) Solving the problem (7.1) using MOSEK will result in a solution, a solution status and a problem status. Among the log output from the execution of MOSEK on the above problem are the lines: Basic solution Problem status : PRIMAL INFEASIBLE Solution status : PRIMAL INFEASIBLE CER The first line indicates that the problem status is primal infeasible. The second line says that a certificate of the infeasibility was found. The certificate is returned in place of the solution to the problem. 7.2.2 Locating the cause of primal infeasibility Usually a primal infeasible problem status is caused by a mistake in formulating the problem and therefore the question arises: ”What is the cause of the infeasible status?” When trying to answer this question, it is often advantageous to follow these steps: • Remove the objective function. This does not change the infeasible status but simplifies the problem, eliminating any possibility of problems related to the objective function. • Consider whether your problem has some necessary conditions for feasibility and examine if these are satisfied, e.g. total supply should be greater than or equal to total demand. • Verify that coefficients and bounds are reasonably sized in your problem. If the problem is still primal infeasible, some of the constraints must be relaxed or removed completely. The MOSEK infeasibility report (Section 7.2.4) may assist you in finding the constraints causing the infeasibility. Possible ways of relaxing your problem include: • Increasing (decreasing) upper (lower) bounds on variables and constraints. • Removing suspected constraints from the problem. Returning to the transportation example, we discover that removing the fifth constraint x 12 = 200
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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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CONTENTS xi 9.2.171 MSK IPAR SOL RE
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CONTENTS xiii 11.29 Ordering strate
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CONTENTS xv 18.2 arki001 . . . . .
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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. OPTIMIZATION TOOLBOX FOR MATLA
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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
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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
Page 61 and 62: 5.5. NONLINEAR CONVEX OPTIMIZATION
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Page 69 and 70: 6.5. TERMINATION CRITERION 53 The f
Page 71 and 72: 6.7. UNDERSTANDING SOLUTION QUALITY
Page 73 and 74: Chapter 7 The analyzers 7.1 The pro
Page 75 and 76: 7.1. THE PROBLEM ANALYZER 59 Constr
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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.
Page 99 and 100: 83 • MSK DPAR INTPNT NL TOL REL G
Page 101 and 102: 85 • MSK IPAR LOG MIO. Controls t
Page 103 and 104: 87 • MSK DPAR INTPNT NL MERIT BAL
Page 105 and 106: 89 • MSK IPAR INFEAS PREFER PRIMA
Page 107 and 108: 91 • MSK IPAR SIM SAVE LU. Contro
Page 109 and 110: 9.1. MSKDPARAME: DOUBLE PARAMETERS
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9.1. MSKDPARAME: DOUBLE PARAMETERS
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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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The MOSEK command line tool Version 7.0 (Revision 141)

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