The MOSEK optimization tools manual.
Version 6.0 (Revision 135).
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The MOSEK optimization tools manual.
Version 6.0 (Revision 135).
Contact information
License agreement
1. Changes and new features in MOSEK
1.1. Compilers used to build MOSEK
1.2. General changes
1.3. Optimizers
1.3.1. Interior point optimizer
1.3.2. The simplex optimizers
1.3.3. Mixed-integer optimizer
1.4. License system
1.5. Other changes
1.6. Interfaces
1.7. Platform changes
2. The MOSEK optimization tools
2.1. What is MOSEK
2.1.1. Interfaces
2.2. How to use this manual
3. Getting support and help
3.1. MOSEK documentation
3.2. Additional reading
4. Using the MOSEK command line tool
4.1. Getting started
4.2. Examples
4.2.1. Linear optimization
4.2.2. Quadratic optimization
4.2.3. Conic optimization
4.3. Passing options to the command line tool
4.4. Reading and writing problem data files
4.4.1. Reading compressed data files
4.4.2. Converting from one format and to another
4.5. Hot-start
4.5.1. An example
4.6. Further information
4.7. Solution file filtering
5. MOSEK and AMPL
5.1. Invoking the AMPL shell
5.2. Applicability
5.3. An example
5.4. Determining the outcome of an optimization
5.5. Optimizer options
5.5.1. The MOSEK parameter database
5.5.2. Options
5.5.2.1.
outlev
5.5.2.2.
wantsol
5.6. Constraint and variable names
5.7. Which solution is returned to AMPL
5.8. Hot-start
5.9. Conic constraints
5.10. Sensitivity analysis
5.11. Using the command line version of the AMPL interface
6. MOSEK and GAMS
7. MOSEK and MATLAB
8. Interfaces to MOSEK
8.1. The optimizer API
9. Modelling
9.1. Linear optimization
9.1.1. Duality for linear optimization
9.1.1.1. A primal-dual feasible solution
9.1.1.2. An optimal solution
9.1.1.3. Primal infeasible problems
9.1.1.4. Dual infeasible problems
9.1.2. Primal and dual infeasible case
9.2. Quadratic and quadratically constrained optimization
9.2.1. A general recommendation
9.2.2. Reformulating as a separable quadratic problem
9.3. Conic optimization
9.3.1. Duality for conic optimization
9.3.2. Infeasibility
9.3.3. Examples
9.3.3.1. Quadratic objective and constraints
9.3.3.2. Minimizing a sum of norms
9.3.3.3. Modelling polynomial terms using conic optimization
9.3.3.4. Optimization with rational polynomials
9.3.3.5. Convex increasing power functions
9.3.3.6. Decreasing power functions
9.3.3.7. Minimizing general polynomials
9.3.3.8. Further reading
9.3.4. Potential pitfalls in conic optimization
9.3.4.1. Non-attainment in the primal problem
9.3.4.2. Non-attainment in the dual problem
9.4. Nonlinear convex optimization
9.4.1. Duality
9.5. Recommendations
9.5.1. Avoid near infeasible models
9.6. Examples continued
9.6.1. The absolute value
9.6.2. The Markowitz portfolio model
9.6.2.1. Minimizing variance for a given return
9.6.2.2. Conic quadratic reformulation
9.6.2.3. Transaction costs with market impact term
9.6.2.4. Further reading
10. The optimizers for continuous problems
10.1. How an optimizer works
10.1.1. Presolve
10.1.1.1. Eliminator
10.1.1.2. Linear dependency checker
10.1.2. Dualizer
10.1.3. Scaling
10.1.4. Using multiple CPU's
10.2. Linear optimization
10.2.1. Optimizer selection
10.2.2. The interior-point optimizer
10.2.2.1. Interior-point termination criterion
10.2.2.2. Basis identification
10.2.2.3. The interior-point log
10.2.3. The simplex based optimizer
10.2.3.1. Simplex termination criterion
10.2.3.2. Starting from an existing solution
10.2.3.3. Numerical difficulties in the simplex optimizers
10.2.4. The interior-point or the simplex optimizer?
10.2.5. The primal or the dual simplex variant?
10.3. Linear network optimization
10.3.1. Network flow problems
10.3.2. Embedded network problems
10.4. Conic optimization
10.4.1. The interior-point optimizer
10.4.1.1. Interior-point termination criteria
10.5. Nonlinear convex optimization
10.5.1. The interior-point optimizer
10.5.1.1. The convexity requirement
10.5.1.2. The differentiabilty requirement
10.5.1.3. Interior-point termination criteria
10.6. Solving problems in parallel
10.6.1. Thread safety
10.6.2. The parallelized interior-point optimizer
10.6.3. The concurrent optimizer
10.6.3.1. Concurrent optimization from the command line
10.7. Understanding solution quality
10.7.1. The solution summary
10.7.1.1. The optimal case
10.7.1.2. The primal infeasible case
11. The optimizer for mixed integer problems
11.1. Some notation
11.2. An important fact about integer optimization problems
11.3. How the integer optimizer works
11.3.1. Presolve
11.3.2. Heuristic
11.3.3. The optimization phase
11.4. Termination criterion
11.5. How to speed up the solution process
11.6. Understanding solution quality
11.6.1. Solutionsummary
12. The analyzers
12.1. The problem analyzer
12.1.1. General characteristics
12.1.2. Objective
12.1.3. Linear constraints
12.1.4. Constraint and variable bounds
12.1.5. Quadratic constraints
12.1.6. Conic constraints
12.2. Analyzing infeasible problems
12.2.1. Example: Primal infeasibility
12.2.2. Locating the cause of primal infeasibility
12.2.3. Locating the cause of dual infeasibility
12.2.3.1. A cautious note
12.2.4. The infeasibility report
12.2.4.1. Example: Primal infeasibility
12.2.4.2. Example: Dual infeasibility
12.2.5. Theory concerning infeasible problems
12.2.6. The certificate of primal infeasibility
12.2.7. The certificate of dual infeasibility
13. Feasibility repair
13.1. The main idea
13.2. Feasibility repair in MOSEK
13.2.1. Usage of negative weights
13.2.2. Automatical naming
13.2.3. An example
14. Sensitivity analysis
14.1. Introduction
14.2. Restrictions
14.3. References
14.4. Sensitivity analysis for linear problems
14.4.1. The optimal objective value function
14.4.1.1. Equality constraints
14.4.2. The basis type sensitivity analysis
14.4.3. The optimal partition type sensitivity analysis
14.4.4. An example
14.5. Sensitivity analysis with the command line tool
14.5.1. Sensitivity analysis specification file
14.5.2. Example: Sensitivity analysis from command line
14.5.3. Controlling log output
A. MOSEK command line tool reference
A.1. Introduction
A.2. Command line arguments
A.3. The parameter file
A.3.1. Using the parameter file
B. The MPS file format
B.1. The MPS file format
B.1.1. An example
B.1.2.
NAME
B.1.3.
OBJSENSE
(optional)
B.1.4.
OBJNAME
(optional)
B.1.5.
ROWS
B.1.6.
COLUMNS
B.1.7.
RHS
(optional)
B.1.8.
RANGES
(optional)
B.1.9.
QSECTION
(optional)
B.1.10.
BOUNDS
(optional)
B.1.11.
CSECTION
(optional)
B.1.12.
ENDATA
B.2. Integer variables
B.3. General limitations
B.4. Interpretation of the MPS format
B.5. The free MPS format
C. The LP file format
C.1. A warning
C.2. The LP file format
C.2.1. The sections
C.2.1.1. The objective
C.2.1.2. The constraints
C.2.1.3. Bounds
C.2.1.4. Variable types
C.2.1.5. Terminating section
C.2.1.6. An example
C.2.2. LP format peculiarities
C.2.2.1. Comments
C.2.2.2. Names
C.2.2.3. Variable bounds
C.2.2.4. MOSEK specific extensions to the LP format
C.2.3. The strict LP format
C.2.4. Formatting of an LP file
C.2.4.1. Speeding up file reading
C.2.4.2. Unnamed constraints
D. The OPF format
D.1. Intended use
D.2. The file format
D.2.1. Sections
D.2.2. Numbers
D.2.3. Names
D.3. Parameters section
D.4. Writing OPF files from MOSEK
D.5. Examples
D.5.1. Linear example
lo1.opf
D.5.2. Quadratic example
qo1.opf
D.5.3. Conic quadratic example
cqo1.opf
D.5.4. Mixed integer example
milo1.opf
E. The XML (OSiL) format
F. The solution file format
F.1. The basic and interior solution files
F.2. The integer solution file
G. The ORD file format
G.1. An example
H. Parameters reference
H.1. Parameter groups
H.1.1. Logging parameters.
H.1.2. Basis identification parameters.
H.1.3. The Interior-point method parameters.
H.1.4. Simplex optimizer parameters.
H.1.5. Primal simplex optimizer parameters.
H.1.6. Dual simplex optimizer parameters.
H.1.7. Network simplex optimizer parameters.
H.1.8. Nonlinear convex method parameters.
H.1.9. The conic interior-point method parameters.
H.1.10. The mixed-integer optimization parameters.
H.1.11. Presolve parameters.
H.1.12. Termination criterion parameters.
H.1.13. Progress call-back parameters.
H.1.14. Non-convex solver parameters.
H.1.15. Feasibility repair parameters.
H.1.16. Optimization system parameters.
H.1.17. Output information parameters.
H.1.18. Extra information about the optimization problem.
H.1.19. Overall solver parameters.
H.1.20. Behavior of the optimization task.
H.1.21. Data input/output parameters.
H.1.22. Analysis parameters.
H.1.23. Solution input/output parameters.
H.1.24. Infeasibility report parameters.
H.1.25. License manager parameters.
H.1.26. Data check parameters.
H.1.27. Debugging parameters.
H.2. Double parameters
H.3. Integer parameters
H.4. String parameter types
I. Symbolic constants reference
I.1. Constraint or variable access modes
I.2. Function opcode
I.3. Function operand type
I.4. Basis identification
I.5. Bound keys
I.6. Specifies the branching direction.
I.7. Progress call-back codes
I.8. Types of convexity checks.
I.9. Compression types
I.10. Cone types
I.11. CPU type
I.12. Data format types
I.13. Double information items
I.14. Double parameters
I.15. Feasibility repair types
I.16. License feature
I.17. Integer information items.
I.18. Information item types
I.19. Input/output modes
I.20. Integer parameters
I.21. Language selection constants
I.22. Long integer information items.
I.23. Mark
I.24. Continuous mixed-integer solution type
I.25. Integer restrictions
I.26. Mixed-integer node selection types
I.27. MPS file format type
I.28. Message keys
I.29. Network detection method
I.30. Objective sense types
I.31. On/off
I.32. Optimizer types
I.33. Ordering strategies
I.34. Parameter type
I.35. Presolve method.
I.36. Problem data items
I.37. Problem types
I.38. Problem status keys
I.39. Interpretation of quadratic terms in MPS files
I.40. Response codes
I.41. Response code type
I.42. Scaling type
I.43. Scaling type
I.44. Sensitivity types
I.45. Degeneracy strategies
I.46. Exploit duplicate columns.
I.47. Hot-start type employed by the simplex optimizer
I.48. Problem reformulation.
I.49. Simplex selection strategy
I.50. Solution items
I.51. Solution status keys
I.52. Solution types
I.53. Solve primal or dual form
I.54. String parameter types
I.55. Status keys
I.56. Starting point types
I.57. Stream types
I.58. Integer values
I.59. Variable types
I.60. XML writer output mode
J. Problem analyzer examples
J.1. air04
J.2. arki001
J.3. Problem with both linear and quadratic constraints
J.4. Problem with both linear and conic constraints
Bibliography
Index
The MOSEK optimization tools manual.
Version 6.0 (Revision 135).
Up :
'Documentation Help'
Next :
Contact information
Contents
Index
Wed Feb 29 16:20:57 2012