8 The Optimizers for Continuous ProblemsΒΆ

The most essential part of MOSEK are the optimizers. This chapter describes the optimizers for the class of continuous problems without integer variables, that is:

  • linear problems,
  • conic problems (quadratic and semidefinite),
  • general convex problems.

MOSEK offers an interior-point optimizer for each class of problems and also a simplex optimizer for linear problems. The structure of a successful optimization process is roughly:

  • Presolve
    1. Elimination: Reduce the size of the problem.
    2. Dualizer: Choose whether to solve the primal or the dual form of the problem.
    3. Scaling: Scale the problem for better numerical stability.
  • Optimization
    1. Optimize: Solve the problem using selected method.
    2. Terminate: Stop the optimization when specific termination criteria have been met.
    3. Report: Return the solution or an infeasibility certificate.

The preprocessing stage is transparent to the user, but useful to know about for tuning purposes. The purpose of the preprocessing steps is to make the actual optimization more efficient and robust. We discuss the details of the above steps in the following sections.