Modeling guide for MP-based AMPL solvers

Ever wondered how to model logical and non-linear constraints? For example:

• At most one of the variables x, y can be positive

• All variables in a group should have different values

• Piecewise-linear approximation of y = sin(x).

MP automates many of such modeling tasks by reformulating AMPL models suitably for the given solver. Moreover, MP supports Multiple objectives. A series of small modeling tasks like these are handled in the MP Modeling Series, while below follows a comprehensive guide.

• Modeling guide for MP-based AMPL solvers
• Modeling overview and implemented solvers
• Expressions supported
  • Conditional operators
  • Logical operators
  • Piecewise-linear expressions
  • Counting operators
  • Relational and comparison operators
  • Complementarity operator
  • Set membership operator
  • Quadratic and power operators
  • Conic optimization
  • General nonlinear functions
• Multiple objectives
  • Blended objectives
  • Lexicographical objectives
  • Examples
• Efficiency considerations
  • Simplification of logic
  • Creation of common subexpressions
  • Bounds on subexpressions
• Numerical accuracy
  • Tight coefficients
  • Importance of tight bounds: “big-M” constraints
  • Piecewise-linear functions
• Tools & details
  • Reformulation settings
  • Explore the reformulations
  • Automatic solution check
• Troubleshooting