The MOSEK optimization toolbox for MATLAB manual.
Version 5.0 (Revision 138).
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The MOSEK optimization toolbox for MATLAB manual.
Version 5.0 (Revision 138).
Contact information
License agreement
1. Changes and new features in MOSEK
1.1. File formats
1.2. Optimizers
1.3. API changes
1.4. License system
1.5. Other changes
1.6. Interfaces
1.7. Supported platforms
2. Introduction
2.1. What is optimization
2.2. Why you need the MOSEK optimization toolbox
2.2.1. Features of the MOSEK optimization toolbox
2.3. Comparison with the MATLAB optimization toolbox
3. Installation
3.1. Locating the toolbox functions
3.1.1. On Windows
3.1.2. On Linux/UNIX/MAC OSX
3.1.3. Permanently changing
matlabpath
3.2. Verifying MOSEK works
3.3. Troubleshooting
3.3.1. ??? Undefined function or variable 'mosekopt'
3.3.1.1. Unable to load mex file
3.3.2.
libgcc_s.so.1 must be installed for pthread_cancel to work
3.3.3. Compiling with the MATLAB compiler
3.3.4. Shadows the M-file
3.3.5. Cannot find authentication file
4. Getting support and help
4.1. MOSEK documentation
4.2. Additional reading
5. MOSEK / MATLAB integration
5.1. MOSEK replacements for MATLAB functions
5.2. The license system
6. A guided tour
6.1. Introduction
6.2. The tour starts
6.3. The MOSEK terminolgy
6.4. Linear optimization
6.4.1. Using
msklpopt
6.4.2. Using
mosekopt
6.5. Convex quadratic optimization
6.5.1. Two important assumptions
6.5.2. Using
mskqpopt
6.5.3. Using
mosekopt
6.6. Conic optimization
6.6.1. The conic optimization problem
6.6.2. Solving an example
6.6.3. Quadratic and conic optimization
6.6.4. Conic duality and the dual solution
6.6.4.1. How to obtain the dual solution
6.6.5. Setting accuracy parameters for the conic optimizer
6.7. Quadratically constrained optimization
6.8. Linear least squares and related norm minimization problems
6.8.1. The case of the 2 norm
6.8.2. The case of the infinity norm
6.8.3. The case of the one norm
6.8.3.1. A better formulation
6.9. More about solving linear least squares problems
6.9.1. Using conic optimization linear least squares problems
6.10. Entropy optimization
6.10.1. Using
mskenopt
6.11. Geometric optimization
6.11.1. Using
mskgpopt
6.11.2. Comments
6.11.2.1. Solving large scale problems
6.11.2.2. Preprocessing tip
6.12. Separable convex optimization
6.12.1. Using
mskscopt
6.13. Mixed integer optimization
6.13.1. Solving an example
6.13.2. Speeding up the solution of a mixed integer problem
6.13.2.1. Specifying an initial feasible solution
6.13.2.2. Using branching priorities
6.14. Sensitivity analysis
6.15. The solutions
6.15.1. The constraint and variable status keys
6.16. Viewing the task information
6.17. Inspecting and setting parameters
6.18. Advanced start (warmstart)
6.18.1. Some examples using warmstart
6.18.2. Adding a new variable
6.18.3. Fixing a variable
6.18.4. Adding a new constraint
6.18.5. Using numeric values to represent status key codes
6.19. Using names
6.19.1. Blanks in names
6.20. MPS files
6.20.1. Reading a MPS file
6.20.2. Writing a MPS files
6.21. User call-back functions
6.21.1. Controlling log printing via call-back
6.21.2. The iteration call-back function
7. Command reference
7.1. Data structures
7.1.1.
prob
7.1.2.
names
7.1.3.
cones
7.1.4.
sol
7.1.5.
prisen
7.1.6.
duasen
7.1.7.
info
7.1.8.
symbcon
7.1.9.
callback
7.2. An example of a command reference
7.3. Functions provided by the MOSEK optimization toolbox
7.4. MATLAB optimization toolbox compatible functions
7.4.1. For linear and quadratic optimization
7.4.2. For linear least squares problems
7.4.3. The optimization options
7.4.3.1. Viewing and modifying the optimization options
8. Case studies
8.1. Robust linear optimization
8.1.1. Introductory example
8.1.2. Data uncertainty and its consequences.
8.1.3. Robust linear optimization methodology
8.1.3.1. Uncertain linear programs and their robust counterparts.
8.1.3.2. Robust counterpart of uncertain of a linear optimization problem with interval uncertainty.
Introductory example (continued).
8.1.4. Random uncertainty and Ellipsoidal Robust Counterpart
8.1.4.1. Example: Interval and Ellipsoidal Robust counterparts of uncertain linear constraint with independent random perturbations of coefficients.
8.1.4.1.1. Combined Interval-Ellipsoidal Robust Counterpart.
8.1.5. Further references
8.2. Geometric (posynomial) optimization
8.2.1. The problem
8.2.2. Applications
8.2.3. Modelling tricks
8.2.3.1. Equalities
8.2.4. Problematic formulations
8.2.4.1. Finite unattainable solution
8.2.4.2. Infinite solution
8.2.5. An example
8.2.6. Solving the example
8.2.7. Exporting to a file
8.2.8. Further information
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. Linear network flow problems
9.3. Quadratic and quadratically constrained optimization
9.3.1. A general recommendation
9.3.2. Reformulating as a separable quadratic problem
9.4. Conic optimization
9.4.1. Duality for conic optimization
9.4.2. The dual of the dual
9.4.3. Infeasibility
9.4.4. Examples
9.4.4.1. Quadratic objective and constraints
9.4.4.2. Minimizing a sum of norms
9.4.4.3. Modelling polynomial terms using conic optimization
9.4.4.4. Further reading
9.4.5. Potential pitfalls in conic optimization
9.4.5.1. Non-attainment in the primal problem
9.4.5.2. Non-attainment in the dual problem
9.5. Nonlinear convex optimization
9.5.1. Duality
9.6. Recommendations
9.6.1. Avoid nearly infeasible models
9.7. Examples continued
9.7.1. The absolute value
9.7.2. The Markowitz portfolio model
9.7.2.1. Minimizing variance for a given return
9.7.2.2. Conic quadratic reformulation.
9.7.2.3. Transaction costs with market impact term
9.7.2.4. Further reading
10. The optimizers for continuous problems
10.1. How an optimizer works
10.1.1. Presolve
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. Basis identification
10.2.2.2. Interior-point termination criterion
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. 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 through the API
10.6.4. A more flexible concurrent optimizer
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
12. Analyzing infeasible problems
12.1. Example: Primal infeasibility
12.1.1. Locating the cause of primal infeasibility
12.1.2. Locating the cause of dual infeasibility
12.1.2.1. A cautious note
12.1.3. The infeasibility report
12.1.3.1. Example: Primal infeasibility
12.1.3.2. Example: Dual infeasibility
12.2. Theory concerning infeasible problems
12.2.1. Certificat of primal infeasibility
12.2.2. Certificat of dual infeasibility
13. Sensitivity analysis
13.1. Introduction
13.2. Restrictions
13.3. References
13.4. Sensitivity analysis for linear problems
13.4.1. The optimal objective value function
13.4.1.1. Equality constraints
13.4.2. The basis type sensitivity analysis
13.4.3. The optimal partition type sensitivity analysis
13.4.4. An example
13.5. Sensitivity analysis in the MATLAB toolbox
13.5.1. On bounds
13.5.1.1. prisen
13.5.1.2. duasen
13.5.2. Selecting analysis type
13.5.3. An example
A. The MPS file format
A.1. The MPS file format
A.1.1. An example
A.1.2.
NAME
A.1.3.
OBJSENSE
(optional)
A.1.4.
OBJNAME
(optional)
A.1.5.
ROWS
A.1.6.
COLUMNS
A.1.7.
RHS
(optional)
A.1.8.
RANGES
(optional)
A.1.9.
QSECTION
(optional)
A.1.10.
BOUNDS
(optional)
A.1.11.
CSECTION
(optional)
A.1.12.
ENDATA
A.2. Integer variables
A.3. General limitations
A.4. Interpretation of the MPS format
A.5. The free MPS format
B. The LP file format
B.1. A warning
B.2. The LP file format
B.2.1. The sections
B.2.1.1. The objective
B.2.1.2. The constraints
B.2.1.3. Bounds
B.2.1.4. Variable types
B.2.1.5. Terminating section
B.2.1.6. An example
B.2.2. LP format peculiarities
B.2.2.1. Comments
B.2.2.2. Names
B.2.2.3. Variable bounds
B.2.2.4. MOSEK specific extensions to the LP format
B.2.3. The strict LP format
B.2.4. Formatting of an LP file
B.2.4.1. Speeding up file reading
B.2.4.2. Unnamed constraints
C. Parameters
C.1. Parameter groups
C.1.1. Logging parameters.
C.1.2. Basis identification parameters.
C.1.3. The Interior-point method parameters.
C.1.4. Simplex optimizer parameters.
C.1.5. Primal simplex optimizer parameters.
C.1.6. Dual simplex optimizer parameters.
C.1.7. Network simplex optimizer parameters.
C.1.8. Nonlinear convex method parameters.
C.1.9. The conic interior-point method parameters.
C.1.10. The mixed integer optimization parameters.
C.1.11. Presolve parameters.
C.1.12. Termination criterion parameters.
C.1.13. Progress call-back parameters.
C.1.14. Non-convex solver parameters.
C.1.15. Feasibility repair parameters.
C.1.16. Optimization system parameters.
C.1.17. Output information parameters.
C.1.18. Extra information about the optimization problem.
C.1.19. Overall solver parameters.
C.1.20. Behavior of the optimization task.
C.1.21. Data input/output parameters.
C.1.22. Solution input/output parameters.
C.1.23. Infeasibility report parameters.
C.1.24. License manager parameters.
C.1.25. Data check parameters.
C.2. Double parameters
C.3. Integer parameters
C.4. String parameter types
D. Symbolic constants
D.1. Constraint or variable access modes
D.2. Basis identification
D.3. Bound keys
D.4. Specifies the branching direction.
D.5. Progress call-back codes
D.6. Types of convexity checks.
D.7. Compression types
D.8. Cone types
D.9. CPU type
D.10. Data format types
D.11. Double information items
D.12. Double parameters
D.13. Double values
D.14. Feasibility repair types
D.15. Integer information items.
D.16. Information item types
D.17. Input/output modes
D.18. Integer parameters
D.19. Bound keys
D.20. Continuous mixed integer solution type
D.21. Integer restrictions
D.22. Mixed integer node selection types
D.23. MPS file format type
D.24. Message keys
D.25. Network detection method
D.26. Objective sense types
D.27. On/off
D.28. Optimizer types
D.29. Ordering strategies
D.30. Parameter type
D.31. Presolve method.
D.32. Problem data items
D.33. Problem types
D.34. Problem status keys
D.35. Interpretation of quadratic terms in MPS files
D.36. Response codes
D.37. Response code type
D.38. Scaling type
D.39. Sensitivity types
D.40. Degeneracy strategies
D.41. Hot-start type employed by the simplex optimizer
D.42. Simplex selection strategy
D.43. Solution items
D.44. Solution status keys
D.45. Solution types
D.46. Solve primal or dual form
D.47. String parameter types
D.48. Status keys
D.49. Starting point types
D.50. Stream types
D.51. Integer values
D.52. Variable types
D.53. XML writer output mode
Bibliography
Index
The MOSEK optimization toolbox for MATLAB manual.
Version 5.0 (Revision 138).
Up :
'Documentation Help'
Next :
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Contents
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Mon Sep 14 15:56:18 2009